>> YOUR LINK HERE: ___ http://youtube.com/watch?v=UTxG9Fy6o-c
Proving a compound proposition is a tautology","styleRuns":[{"startIndex":0,"length":45,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":45,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CNgBELsvGAIiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC1VUeEc5Rnk2by1jGAYyJSIRIgtVVHhHOUZ5Nm8tYzAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CNgBELsvGAIiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CNcBELovIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"tDH67yRNXzI","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/tDH67yRNXzI/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBJ15Qz2sV2tuHXXkY680jrRcgYOg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/tDH67yRNXzI/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLB5ZnN1Z2sn3-OnRwiIwWy5f6gohw","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Propositional Logic − Logical Equivalences by Neso Academy 928,081 views 6 years ago 17 minutes"}},"simpleText":"Propositional Logic − Logical Equivalences"},"longBylineText":{"runs":[{"text":"Neso Academy","navigationEndpoint":{"clickTrackingParams":"CNEBEKQwGAAiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@nesoacademy","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCQYMhOMi_Cdj1CEAU-fv80A","canonicalBaseUrl":"/@nesoacademy"}}}]},"publishedTimeText":{"simpleText":"6 years ago"},"viewCountText":{"simpleText":"928,081 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"17 minutes, 23 seconds"}},"simpleText":"17:23"},"navigationEndpoint":{"clickTrackingParams":"CNEBEKQwGAAiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWRI58fq5cXekZ5RmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=tDH67yRNXzI","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"tDH67yRNXzI","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=b431faef244d5f32 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1917500 mt=1740539586 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Neso Academy","navigationEndpoint":{"clickTrackingParams":"CNEBEKQwGAAiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@nesoacademy","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCQYMhOMi_Cdj1CEAU-fv80A","canonicalBaseUrl":"/@nesoacademy"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/1iRrlRhV7RMLlyeLSeYaHjtvql01jATABgZtWeX3GyFcJJNNYp3ICYPgdyUOE6U4Y4PLXee594Q=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CNEBEKQwGAAiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CNEBEKQwGAAiEwiW1_WLsOCLAxWPQXoFHWr1IYJAsr61ovLd_pi0AQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"928K views"}},"simpleText":"928K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CNUBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNUBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"tDH67yRNXzI","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNUBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["tDH67yRNXzI"],"params":"CAQ%3D"}},"videoIds":["tDH67yRNXzI"]}},{"clickTrackingParams":"CNUBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CNYBELlqIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},"popupType":"TOAST"}}]}},"trackingParams":"CNUBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CNEBEKQwGAAiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgt0REg2N3lSTlh6SQ%3D%3D","commands":[{"clickTrackingParams":"CNEBEKQwGAAiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CNQBEI5iIhMIltf1i7DgiwMVj0F6BR1q9SGC","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CNEBEKQwGAAiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","hasSeparator":true}}],"trackingParams":"CNEBEKQwGAAiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"17 minutes, 23 seconds"}},"simpleText":"17:23"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNMBEPnnAxgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"tDH67yRNXzI","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CNMBEPnnAxgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"tDH67yRNXzI"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNMBEPnnAxgCIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNIBEMfsBBgDIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNIBEMfsBBgDIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"tDH67yRNXzI","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNIBEMfsBBgDIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["tDH67yRNXzI"],"params":"CAQ%3D"}},"videoIds":["tDH67yRNXzI"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNIBEMfsBBgDIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Propositional Logic − Logical Equivalences - 17 minutes - Go to channel - Neso Academy - 928K views - 6 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"MRooF9a1juA","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/MRooF9a1juA/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AH-CYAC0AWKAgwIABABGGUgZShlMA8= rs=AOn4CLBhuJIBHW_-2ics4dL4Lea7X0fWhw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/MRooF9a1juA/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB_gmAAtAFigIMCAAQARhlIGUoZTAP rs=AOn4CLAkKS5HCDo09_a2OlgXkwBVooe6cg","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Proving a compound proposition is a tautology part 1 of 2 by Kailee Gray 38,028 views 10 years ago 16 minutes"}},"simpleText":"Proving a compound proposition is a tautology part 1 of 2"},"longBylineText":{"runs":[{"text":"Kailee Gray","navigationEndpoint":{"clickTrackingParams":"CMsBEKQwGAEiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@KaileeGray","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCMJQbUuten6_S7g23-Zluig","canonicalBaseUrl":"/@KaileeGray"}}}]},"publishedTimeText":{"simpleText":"10 years ago"},"viewCountText":{"simpleText":"38,028 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"16 minutes, 5 seconds"}},"simpleText":"16:05"},"navigationEndpoint":{"clickTrackingParams":"CMsBEKQwGAEiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWRI58fq5cXekZ5RmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=MRooF9a1juA","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"MRooF9a1juA","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=311a2817d6b58ee0 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=2182500 mt=1740539586 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Kailee Gray","navigationEndpoint":{"clickTrackingParams":"CMsBEKQwGAEiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@KaileeGray","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCMJQbUuten6_S7g23-Zluig","canonicalBaseUrl":"/@KaileeGray"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lQP8FK6fqgujgooc4Cv9behJd8c4GNcXNkJJbmjSG9OQ=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CMsBEKQwGAEiEwiW1_WLsOCLAxWPQXoFHWr1IYJA4J3Wtf2Cio0x","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"38K views"}},"simpleText":"38K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CM8BEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CM8BEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"MRooF9a1juA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CM8BEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["MRooF9a1juA"],"params":"CAQ%3D"}},"videoIds":["MRooF9a1juA"]}},{"clickTrackingParams":"CM8BEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CNABELlqIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},"popupType":"TOAST"}}]}},"trackingParams":"CM8BEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMsBEKQwGAEiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtNUm9vRjlhMWp1QQ%3D%3D","commands":[{"clickTrackingParams":"CMsBEKQwGAEiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CM4BEI5iIhMIltf1i7DgiwMVj0F6BR1q9SGC","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMsBEKQwGAEiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","hasSeparator":true}}],"trackingParams":"CMsBEKQwGAEiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"16 minutes, 5 seconds"}},"simpleText":"16:05"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CM0BEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"MRooF9a1juA","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CM0BEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"MRooF9a1juA"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CM0BEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMwBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMwBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"MRooF9a1juA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMwBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["MRooF9a1juA"],"params":"CAQ%3D"}},"videoIds":["MRooF9a1juA"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMwBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Proving a compound proposition is a tautology part 1 of 2 - 16 minutes - Go to channel - Kailee Gray - 38K views - 10 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/MRooF9a1juA/mqdefault_6s.webp?du=3000 sqp=CNDg-b0G rs=AOn4CLDZe4KfpjsDP8BxtjXLWzRkEuwchg","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"xZ93paAW_fk","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/xZ93paAW_fk/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLDQrxr6U8z629sGSTdBWFzCIgXf3w","width":168,"height":94},{"url":"https://i.ytimg.com/vi/xZ93paAW_fk/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBygJJLE9bSkdmwa74Q1mwMW6dyoQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"MAT 160 Section 1.3 Propositional Equivalences by Gilbert Eyabi 15,201 views 7 years ago 21 minutes"}},"simpleText":"MAT 160 Section 1.3 Propositional Equivalences"},"longBylineText":{"runs":[{"text":"Gilbert Eyabi","navigationEndpoint":{"clickTrackingParams":"CMUBEKQwGAIiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@gilberteyabi6574","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCt2u7AQNIDgVCcMHbbxNylg","canonicalBaseUrl":"/@gilberteyabi6574"}}}]},"publishedTimeText":{"simpleText":"7 years ago"},"viewCountText":{"simpleText":"15,201 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"21 minutes, 43 seconds"}},"simpleText":"21:43"},"navigationEndpoint":{"clickTrackingParams":"CMUBEKQwGAIiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWRI58fq5cXekZ5RmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=xZ93paAW_fk","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"xZ93paAW_fk","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=c59f77a5a016fdf9 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=2182500 mt=1740539586 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Gilbert Eyabi","navigationEndpoint":{"clickTrackingParams":"CMUBEKQwGAIiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@gilberteyabi6574","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCt2u7AQNIDgVCcMHbbxNylg","canonicalBaseUrl":"/@gilberteyabi6574"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_ltvUufGkOKH12YReQb8Dv2gQ31tRWdV4Zraq4rBToUTg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CMUBEKQwGAIiEwiW1_WLsOCLAxWPQXoFHWr1IYJA-fvbgNr03c_FAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"15K views"}},"simpleText":"15K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMkBEP6YBBgFIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMkBEP6YBBgFIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"xZ93paAW_fk","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMkBEP6YBBgFIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["xZ93paAW_fk"],"params":"CAQ%3D"}},"videoIds":["xZ93paAW_fk"]}},{"clickTrackingParams":"CMkBEP6YBBgFIhMIltf1i7DgiwMVj0F6BR1q9SGC","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMoBELlqIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},"popupType":"TOAST"}}]}},"trackingParams":"CMkBEP6YBBgFIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMUBEKQwGAIiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgt4WjkzcGFBV19maw%3D%3D","commands":[{"clickTrackingParams":"CMUBEKQwGAIiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMgBEI5iIhMIltf1i7DgiwMVj0F6BR1q9SGC","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMUBEKQwGAIiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","hasSeparator":true}}],"trackingParams":"CMUBEKQwGAIiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"21 minutes, 43 seconds"}},"simpleText":"21:43"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMcBEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"xZ93paAW_fk","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMcBEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"xZ93paAW_fk"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMcBEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMYBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMYBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"xZ93paAW_fk","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMYBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["xZ93paAW_fk"],"params":"CAQ%3D"}},"videoIds":["xZ93paAW_fk"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMYBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"MAT 160 Section 1.3 Propositional Equivalences - 21 minutes - Go to channel - Gilbert Eyabi - 15K views - 7 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"nybpGnainWM","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/nybpGnainWM/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AH-CYAC0AWKAgwIABABGGUgZShlMA8= rs=AOn4CLD3SMwG-laEBdwRdVPQ7Ytf_xk-YA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/nybpGnainWM/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB_gmAAtAFigIMCAAQARhlIGUoZTAP rs=AOn4CLB5VTDCnWWsg-CY6eMJVswkuL1XSA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Logical Equivalence (Part 1) by Juan Paulo Jurada 7,478 views 1 year ago 17 minutes"}},"simpleText":"Logical Equivalence (Part 1)"},"longBylineText":{"runs":[{"text":"Juan Paulo Jurada","navigationEndpoint":{"clickTrackingParams":"CL8BEKQwGAMiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@juanpaulojurada7164","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCmgNcIeAYXHCGnWo5w7vtyg","canonicalBaseUrl":"/@juanpaulojurada7164"}}}]},"publishedTimeText":{"simpleText":"1 year ago"},"viewCountText":{"simpleText":"7,478 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"17 minutes, 2 seconds"}},"simpleText":"17:02"},"navigationEndpoint":{"clickTrackingParams":"CL8BEKQwGAMiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWRI58fq5cXekZ5RmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=nybpGnainWM","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"nybpGnainWM","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=9f26e91a76a29d63 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=2182500 mt=1740539586 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Juan Paulo Jurada","navigationEndpoint":{"clickTrackingParams":"CL8BEKQwGAMiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@juanpaulojurada7164","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCmgNcIeAYXHCGnWo5w7vtyg","canonicalBaseUrl":"/@juanpaulojurada7164"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_ngqJkMo7nxhJ5XxW8K9eY-hgTf-wslPprbF09Mmz-klic=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CL8BEKQwGAMiEwiW1_WLsOCLAxWPQXoFHWr1IYJA47qKtaejupOfAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"7.4K views"}},"simpleText":"7.4K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMMBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMMBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"nybpGnainWM","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMMBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["nybpGnainWM"],"params":"CAQ%3D"}},"videoIds":["nybpGnainWM"]}},{"clickTrackingParams":"CMMBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMQBELlqIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},"popupType":"TOAST"}}]}},"trackingParams":"CMMBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CL8BEKQwGAMiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtueWJwR25haW5XTQ%3D%3D","commands":[{"clickTrackingParams":"CL8BEKQwGAMiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMIBEI5iIhMIltf1i7DgiwMVj0F6BR1q9SGC","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CL8BEKQwGAMiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","hasSeparator":true}}],"trackingParams":"CL8BEKQwGAMiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"17 minutes, 2 seconds"}},"simpleText":"17:02"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMEBEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"nybpGnainWM","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMEBEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"nybpGnainWM"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMEBEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMABEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMABEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"nybpGnainWM","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMABEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["nybpGnainWM"],"params":"CAQ%3D"}},"videoIds":["nybpGnainWM"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMABEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Logical Equivalence (Part 1) - 17 minutes - Go to channel - Juan Paulo Jurada - 7.4K views - 1 year ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/nybpGnainWM/mqdefault_6s.webp?du=3000 sqp=CM3Z-b0G rs=AOn4CLBZtW1pLhgONFZqgiVWjU-1bzKEiA","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"gduSQrc2IkA","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/gduSQrc2IkA/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBq9wUs93KtzHetExBGyKF1x6UtkQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/gduSQrc2IkA/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLCMYsOXx1NATjBBFmTO_ihJxkpvZw","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Proofs with Rules of Inference 1 (Propositional Logic for Linguists 15) by Dr. Isabel the Linguist 136,266 views 5 years ago 7 minutes, 16 seconds"}},"simpleText":"Proofs with Rules of Inference 1 (Propositional Logic for Linguists 15)"},"longBylineText":{"runs":[{"text":"Dr. Isabel the Linguist","navigationEndpoint":{"clickTrackingParams":"CLkBEKQwGAQiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@isabelthelinguist","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UClKggY1-IVjYMdBE-4ZidjA","canonicalBaseUrl":"/@isabelthelinguist"}}}]},"publishedTimeText":{"simpleText":"5 years ago"},"viewCountText":{"simpleText":"136,266 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"7 minutes, 16 seconds"}},"simpleText":"7:16"},"navigationEndpoint":{"clickTrackingParams":"CLkBEKQwGAQiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWRI58fq5cXekZ5RmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=gduSQrc2IkA","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"gduSQrc2IkA","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=81db9242b7362240 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=2182500 mt=1740539586 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Dr. Isabel the Linguist","navigationEndpoint":{"clickTrackingParams":"CLkBEKQwGAQiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@isabelthelinguist","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UClKggY1-IVjYMdBE-4ZidjA","canonicalBaseUrl":"/@isabelthelinguist"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/zQmglQA5YjIsp0Vg1vxEBMNKTS0ucxKXQdHUvBL5ivtJJ2hyH6UVxwqJKWw5ZFa7ne9eOSWBjbI=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CLkBEKQwGAQiEwiW1_WLsOCLAxWPQXoFHWr1IYJAwMTYuavI5O2BAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"136K views"}},"simpleText":"136K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CL0BEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CL0BEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"gduSQrc2IkA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CL0BEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["gduSQrc2IkA"],"params":"CAQ%3D"}},"videoIds":["gduSQrc2IkA"]}},{"clickTrackingParams":"CL0BEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CL4BELlqIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},"popupType":"TOAST"}}]}},"trackingParams":"CL0BEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLkBEKQwGAQiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtnZHVTUXJjMklrQQ%3D%3D","commands":[{"clickTrackingParams":"CLkBEKQwGAQiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLwBEI5iIhMIltf1i7DgiwMVj0F6BR1q9SGC","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLkBEKQwGAQiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","hasSeparator":true}}],"trackingParams":"CLkBEKQwGAQiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"7 minutes, 16 seconds"}},"simpleText":"7:16"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLsBEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"gduSQrc2IkA","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLsBEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"gduSQrc2IkA"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLsBEPnnAxgBIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLoBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLoBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"gduSQrc2IkA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLoBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["gduSQrc2IkA"],"params":"CAQ%3D"}},"videoIds":["gduSQrc2IkA"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLoBEMfsBBgCIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Proofs with Rules of Inference 1 (Propositional Logic for Linguists 15) - 7 minutes, 16 seconds - Go to channel - Dr. Isabel the Linguist - 136K views - 5 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/gduSQrc2IkA/mqdefault_6s.webp?du=3000 sqp=CODg-b0G rs=AOn4CLC5xiZzS4lLk58bTqp8YlkS16Uidw","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"eihhu72YdpQ","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/eihhu72YdpQ/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLDHwsasjsw6Leftm3zrAwlE9o5s7w","width":168,"height":94},{"url":"https://i.ytimg.com/vi/eihhu72YdpQ/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLASii9SMQCG2cLYZvfn42zdPJH03g","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"LOGIC LAWS - DISCRETE MATHEMATICS by TrevTutor 445,139 views 7 years ago 15 minutes"}},"simpleText":"LOGIC LAWS - DISCRETE MATHEMATICS"},"longBylineText":{"runs":[{"text":"TrevTutor","navigationEndpoint":{"clickTrackingParams":"CLMBEKQwGAUiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@Trevtutor","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCGYSfZbPp3BiAFs531PBY7g","canonicalBaseUrl":"/@Trevtutor"}}}]},"publishedTimeText":{"simpleText":"7 years ago"},"viewCountText":{"simpleText":"445,139 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"15 minutes, 29 seconds"}},"simpleText":"15:29"},"navigationEndpoint":{"clickTrackingParams":"CLMBEKQwGAUiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWRI58fq5cXekZ5RmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=eihhu72YdpQ","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"eihhu72YdpQ","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=7a2861bbbd987694 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=2182500 mt=1740539586 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"TrevTutor","navigationEndpoint":{"clickTrackingParams":"CLMBEKQwGAUiEwiW1_WLsOCLAxWPQXoFHWr1IYIyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@Trevtutor","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCGYSfZbPp3BiAFs531PBY7g","canonicalBaseUrl":"/@Trevtutor"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ozXBkwBDPptThtZjF5hyXcadEzngzVvgHTMTec18pbi5V1G7ZYH5Q1aAKTBvNprKwk2ANuAODg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CLMBEKQwGAUiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CLMBEKQwGAUiEwiW1_WLsOCLAxWPQXoFHWr1IYJAlO3h7Lu3mJR6","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"445K views"}},"simpleText":"445K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLcBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLcBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"eihhu72YdpQ","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLcBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["eihhu72YdpQ"],"params":"CAQ%3D"}},"videoIds":["eihhu72YdpQ"]}},{"clickTrackingParams":"CLcBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CLgBELlqIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},"popupType":"TOAST"}}]}},"trackingParams":"CLcBEP6YBBgGIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLMBEKQwGAUiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtlaWhodTcyWWRwUQ%3D%3D","commands":[{"clickTrackingParams":"CLMBEKQwGAUiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLYBEI5iIhMIltf1i7DgiwMVj0F6BR1q9SGC","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLMBEKQwGAUiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","hasSeparator":true}}],"trackingParams":"CLMBEKQwGAUiEwiW1_WLsOCLAxWPQXoFHWr1IYI=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"15 minutes, 29 seconds"}},"simpleText":"15:29"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLUBEPnnAxgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"eihhu72YdpQ","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLUBEPnnAxgCIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"eihhu72YdpQ"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLUBEPnnAxgCIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLQBEMfsBBgDIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLQBEMfsBBgDIhMIltf1i7DgiwMVj0F6BR1q9SGC","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"eihhu72YdpQ","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLQBEMfsBBgDIhMIltf1i7DgiwMVj0F6BR1q9SGC","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["eihhu72YdpQ"],"params":"CAQ%3D"}},"videoIds":["eihhu72YdpQ"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLQBEMfsBBgDIhMIltf1i7DgiwMVj0F6BR1q9SGC"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"LOGIC LAWS - DISCRETE MATHEMATICS - 15 minutes - Go to channel - TrevTutor - 445K views - 7 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/nyxX2PsdPZU/hqdefault.jpg?sqp=-oaymwEwCKgBEF5IWvKriqkDIwgBFQAAiEIYAfABAfgB_AiAAtAFigIMCAAQARhlIGUoZTAP rs=AOn4CLC-Vlat_YPcw6HrAoVjYdZ2CWKzyA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/nyxX2PsdPZU/hqdefault.jpg?sqp=-oaymwExCNACELwBSFryq4qpAyMIARUAAIhCGAHwAQH4AfwIgALQBYoCDAgAEAEYZSBlKGUwDw== rs=AOn4CLC_R6VYg9xqh1FeR_ED7I2Jm5ix-A","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"13 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":3355443,"darkTheme":3355443}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":4144959,"darkTheme":4144959}}},"stackColor":{"lightTheme":10066329,"darkTheme":9211020}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"CMSC 56 Lec2 - Logical Equivalence"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"a-cube
#############################
