lec10 Proof Strategies I
#############################
Video Source: www.youtube.com/watch?v=D817ZE_NOjg
Proof by contrapositive, Vacuous proof, Proof by contradiction, Direct proofs, Indirect proofs.","styleRuns":[{"startIndex":0,"length":95,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":95,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CMABELsvGAIiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC0Q4MTdaRV9OT2pnGAYyJSIRIgtEODE3WkVfTk9qZzAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CMABELsvGAIiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CL8BELovIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"z1ikaJjZjWI","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/z1ikaJjZjWI/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLDjjQKM5Ta7ltTf4wGp4gYSFWdvPw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/z1ikaJjZjWI/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDlj1J9vZ1SZyVSZHsZkEppFekakg","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"lec09 Rules of Inferences in Predicate Logic by NPTEL - Indian Institute of Science, Bengaluru 5,207 views 3 years ago 45 minutes"}},"simpleText":"lec09 Rules of Inferences in Predicate Logic"},"longBylineText":{"runs":[{"text":"NPTEL - Indian Institute of Science, Bengaluru","navigationEndpoint":{"clickTrackingParams":"CLgBEKQwGAAiEwiG64iZ-cqJAxXXRnoFHVb8EBkyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@nptel-indianinstituteofsci8064","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCc5whtb5eLlPOBxHClAPVUw","canonicalBaseUrl":"/@nptel-indianinstituteofsci8064"}}}]},"publishedTimeText":{"simpleText":"3 years ago"},"viewCountText":{"simpleText":"5,207 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"45 minutes, 53 seconds"}},"simpleText":"45:53"},"navigationEndpoint":{"clickTrackingParams":"CLgBEKQwGAAiEwiG64iZ-cqJAxXXRnoFHVb8EBkyB3JlbGF0ZWRIuPS0_sTs3uYPmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=z1ikaJjZjWI","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"z1ikaJjZjWI","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr2---sn-4g5lznls.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=cf58a46898d98d62 ip=5.34.180.98 initcwndbps=430000 mt=1731007035 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"NPTEL - Indian Institute of Science, Bengaluru","navigationEndpoint":{"clickTrackingParams":"CLgBEKQwGAAiEwiG64iZ-cqJAxXXRnoFHVb8EBkyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@nptel-indianinstituteofsci8064","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCc5whtb5eLlPOBxHClAPVUw","canonicalBaseUrl":"/@nptel-indianinstituteofsci8064"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/X_g_Vm-pNnCD89vB3QL8O58fs-D8vdqSvbduXfrIhLAcJ4Qhln1l0DlY77EjeUZHI61buC4Q=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CLgBEKQwGAAiEwiG64iZ-cqJAxXXRnoFHVb8EBlA4prmxomNqazPAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"5.2K views"}},"simpleText":"5.2K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CL0BEP6YBBgFIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CL0BEP6YBBgFIhMIhuuImfnKiQMV10Z6BR1W_BAZ","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"z1ikaJjZjWI","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CL0BEP6YBBgFIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["z1ikaJjZjWI"],"params":"CAQ%3D"}},"videoIds":["z1ikaJjZjWI"]}},{"clickTrackingParams":"CL0BEP6YBBgFIhMIhuuImfnKiQMV10Z6BR1W_BAZ","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CL4BELlqIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},"popupType":"TOAST"}}]}},"trackingParams":"CL0BEP6YBBgFIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CLwBENGqBRgGIhMIhuuImfnKiQMV10Z6BR1W_BAZ","offlineVideoEndpoint":{"videoId":"z1ikaJjZjWI","onAddCommand":{"clickTrackingParams":"CLwBENGqBRgGIhMIhuuImfnKiQMV10Z6BR1W_BAZ","getDownloadActionCommand":{"videoId":"z1ikaJjZjWI","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CLwBENGqBRgGIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLgBEKQwGAAiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgt6MWlrYUpqWmpXSQ%3D%3D","commands":[{"clickTrackingParams":"CLgBEKQwGAAiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLsBEI5iIhMIhuuImfnKiQMV10Z6BR1W_BAZ","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLgBEKQwGAAiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","hasSeparator":true}}],"trackingParams":"CLgBEKQwGAAiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"45 minutes, 53 seconds"}},"simpleText":"45:53"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLoBEPnnAxgBIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"z1ikaJjZjWI","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLoBEPnnAxgBIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"z1ikaJjZjWI"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLoBEPnnAxgBIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLkBEMfsBBgCIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLkBEMfsBBgCIhMIhuuImfnKiQMV10Z6BR1W_BAZ","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"z1ikaJjZjWI","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLkBEMfsBBgCIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["z1ikaJjZjWI"],"params":"CAQ%3D"}},"videoIds":["z1ikaJjZjWI"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLkBEMfsBBgCIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"lec09 Rules of Inferences in Predicate Logic - 45 minutes - Go to channel - NPTEL - Indian Institute of Science, Bengaluru - 5.2K views - 3 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"HIkIqt_ytdc","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/HIkIqt_ytdc/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCAVEARcLgkWv2BHvJTJC0GN4muEQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/HIkIqt_ytdc/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDHJAOwUVSfT7mYhCXX_4AMzBAonw","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Discrete Math Proofs in 22 Minutes (5 Types, 9 Examples) by TrevTutor 60,616 views 10 months ago 22 minutes"}},"simpleText":"Discrete Math Proofs in 22 Minutes (5 Types, 9 Examples)"},"longBylineText":{"runs":[{"text":"TrevTutor","navigationEndpoint":{"clickTrackingParams":"CLEBEKQwGAEiEwiG64iZ-cqJAxXXRnoFHVb8EBkyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@Trevtutor","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCGYSfZbPp3BiAFs531PBY7g","canonicalBaseUrl":"/@Trevtutor"}}}]},"publishedTimeText":{"simpleText":"10 months ago"},"viewCountText":{"simpleText":"60,616 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"22 minutes, 9 seconds"}},"simpleText":"22:09"},"navigationEndpoint":{"clickTrackingParams":"CLEBEKQwGAEiEwiG64iZ-cqJAxXXRnoFHVb8EBkyB3JlbGF0ZWRIuPS0_sTs3uYPmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=HIkIqt_ytdc","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"HIkIqt_ytdc","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr5---sn-4g5edndl.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=1c8908aadff2b5d7 ip=5.34.180.98 initcwndbps=430000 mt=1731007035 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"TrevTutor","navigationEndpoint":{"clickTrackingParams":"CLEBEKQwGAEiEwiG64iZ-cqJAxXXRnoFHVb8EBkyB3JlbGF0ZWQ=","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/YYQ3p8msQ6ZZcro6cpoyjq3CzBZKJzXSxYT1EmepSUhRE8Ljyw-006-rSXLvCDmBAcQ6syk5Rw=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":"CLEBEKQwGAEiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CLEBEKQwGAEiEwiG64iZ-cqJAxXXRnoFHVb8EBlA1-vK_62VwsQc","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"60K views"}},"simpleText":"60K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLYBEP6YBBgGIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLYBEP6YBBgGIhMIhuuImfnKiQMV10Z6BR1W_BAZ","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"HIkIqt_ytdc","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLYBEP6YBBgGIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["HIkIqt_ytdc"],"params":"CAQ%3D"}},"videoIds":["HIkIqt_ytdc"]}},{"clickTrackingParams":"CLYBEP6YBBgGIhMIhuuImfnKiQMV10Z6BR1W_BAZ","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CLcBELlqIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},"popupType":"TOAST"}}]}},"trackingParams":"CLYBEP6YBBgGIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CLUBENGqBRgHIhMIhuuImfnKiQMV10Z6BR1W_BAZ","offlineVideoEndpoint":{"videoId":"HIkIqt_ytdc","onAddCommand":{"clickTrackingParams":"CLUBENGqBRgHIhMIhuuImfnKiQMV10Z6BR1W_BAZ","getDownloadActionCommand":{"videoId":"HIkIqt_ytdc","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CLUBENGqBRgHIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLEBEKQwGAEiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtISWtJcXRfeXRkYw%3D%3D","commands":[{"clickTrackingParams":"CLEBEKQwGAEiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLQBEI5iIhMIhuuImfnKiQMV10Z6BR1W_BAZ","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLEBEKQwGAEiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","hasSeparator":true}}],"trackingParams":"CLEBEKQwGAEiEwiG64iZ-cqJAxXXRnoFHVb8EBk=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"22 minutes, 9 seconds"}},"simpleText":"22:09"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLMBEPnnAxgCIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"HIkIqt_ytdc","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLMBEPnnAxgCIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"HIkIqt_ytdc"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLMBEPnnAxgCIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLIBEMfsBBgDIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLIBEMfsBBgDIhMIhuuImfnKiQMV10Z6BR1W_BAZ","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"HIkIqt_ytdc","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLIBEMfsBBgDIhMIhuuImfnKiQMV10Z6BR1W_BAZ","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["HIkIqt_ytdc"],"params":"CAQ%3D"}},"videoIds":["HIkIqt_ytdc"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLIBEMfsBBgDIhMIhuuImfnKiQMV10Z6BR1W_BAZ"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Discrete Math Proofs in 22 Minutes (5 Types, 9 Examples) - 22 minutes - Go to channel - TrevTutor - 60K views - 10 months ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/lJ98odiHWso/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLCZq0TfUaFGVs9zxF8mNxGkDeZz3A","width":168,"height":94},{"url":"https://i.ytimg.com/vi/lJ98odiHWso/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLCKrCtYFwOiLjIhRuiGWUbXogOvYA","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"61 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":2630150,"darkTheme":2630150}}}],"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":4996875,"darkTheme":4996875}}},"stackColor":{"lightTheme":12563589,"darkTheme":9209456}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Discrete Mathematics - IIITB"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"NPTEL-NOC IITM
#############################