https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1222/v/what-are-relations-1 2025-03-01T15:52:37.13987578Z What are relations? Using what we know about ordered pairs, and cartesian product of sets, we finally define what a relation is between two sets. We use an example of two sets: one containing living beings and the other containing places to live. We then define terms related to relations: Domain (set of permissible values of input), Range (set of possible values of output) and Codomain (set of permissible values of output). We then touch upon the concept of image (elements from second set) and pre-image (elements from first set). We finally learn how to write relations in set-builder form and roster form. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw What are relations? Using what we know about ordered pairs, and cartesian product of sets, we finally define what a relation is between two sets. We use an example of two sets: one containing living beings and the other containing places to live. We then define terms related to relations: Domain (set of permissible values of input), Range (set of possible values of output) and Codomain (set of permissible values of output). We then touch upon the concept of image (elements from second set) and pre-image (elements from first set). We finally learn how to write relations in set-builder form and roster form. https://cdn.kastatic.org/ka-youtube-converted/22Tc2hE2ATY.mp4/22Tc2hE2ATY.mp4 397 Relations https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1222/v/finding-domain-and-range 2025-03-01T15:52:37.13987578Z Finding domain and range In this worked example, we find domain and range of a relation defined in the set builder form. An essential skill touched in this video is to know how to break down definitions of relations written in set-builder form. We show with an example the usefulness of realising domain and range visually before actually writing things down in roster form. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding domain and range In this worked example, we find domain and range of a relation defined in the set builder form. An essential skill touched in this video is to know how to break down definitions of relations written in set-builder form. We show with an example the usefulness of realising domain and range visually before actually writing things down in roster form. https://cdn.kastatic.org/ka-youtube-converted/hJHATgIrdo0.mp4/hJHATgIrdo0.mp4 282 Relations https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1222/v/worked-example-finding-the-relation 2025-03-01T15:52:37.13987578Z Worked example - Finding the relation How do we work backwards? Can we find the relation in set builder form if we're shown how the elements of both sets connect to each other? We're given a visual representation of the relation and we need to find the domain, range of the relation. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Worked example - Finding the relation How do we work backwards? Can we find the relation in set builder form if we're shown how the elements of both sets connect to each other? We're given a visual representation of the relation and we need to find the domain, range of the relation. https://cdn.kastatic.org/ka-youtube-converted/LnO6WtYfwUQ.mp4/LnO6WtYfwUQ.mp4 239 Relations https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1222/v/total-number-of-possible-relations 2025-03-01T15:52:37.13987578Z Total number of possible relations Given two sets, how do we find ALL possible relations? And when that's too time consuming, can we at least find the number of all possible relations? Let's find out in this video. We use some key principles from the topic - Permutations and Combinations (without actually getting into the terminologies) to navigate our way out of this problem. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Total number of possible relations Given two sets, how do we find ALL possible relations? And when that's too time consuming, can we at least find the number of all possible relations? Let's find out in this video. We use some key principles from the topic - Permutations and Combinations (without actually getting into the terminologies) to navigate our way out of this problem. https://cdn.kastatic.org/ka-youtube-converted/A09vrT1t09U.mp4/A09vrT1t09U.mp4 402 Relations https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-function-intro/v/relations-and-functions 2021-06-30T18:10:09Z Relations and functions Learn to determine if a relation given by a set of ordered pairs is a function. Sal Khan video https://cdn.kastatic.org/googleusercontent/_QXa2dqNYNQ75UOKQ9lalz11LItO7kWgj6mKmI5-Y6VuzzRQgItN43D_HVLYTNTL7D_icdCyMGdWyFRqI61ftbeF Relations and functions Learn to determine if a relation given by a set of ordered pairs is a function. https://cdn.kastatic.org/ka-youtube-converted/Uz0MtFlLD-k.mp4/Uz0MtFlLD-k.mp4 417 Relations https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1222/e/relations 2026-04-07T23:55:07.30621384Z Relations Find relations between two sets in roster form, identify algebraic relationship from roster form. exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1222/e/domain-of-relations 2026-04-07T22:23:57.656416987Z Domain of relations Find domain. exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1222/e/codomain-and-range-of-relations 2026-04-08T00:16:02.937952483Z Codomain and range of relations codomain and range exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1222/e/domain-and-range-of-relations-infinite-sets 2025-03-01T15:52:37.13987578Z Domain and range of relations (infinite sets) Find domain and range when the relation is from an infinite set to an infinite set. exercise