https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1219/v/what-are-ordered-pairs 2025-03-01T15:52:37.13987578Z What are Ordered pairs? Before we begin the unit, let's discuss an important question - What are ordered pairs? They are pairs of objects put in a specific order. We discuss examples of situations where order matters from non-math world as well as the math world. We also take note of the notation used to represent ordered pairs before solving a worked example on the same. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw What are Ordered pairs? Before we begin the unit, let's discuss an important question - What are ordered pairs? They are pairs of objects put in a specific order. We discuss examples of situations where order matters from non-math world as well as the math world. We also take note of the notation used to represent ordered pairs before solving a worked example on the same. https://cdn.kastatic.org/ka-youtube-converted/jQUrfmX0uko.mp4/jQUrfmX0uko.mp4 268 Cartesian product of sets https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1219/v/cartesian-product-of-sets 2025-03-01T15:52:37.13987578Z Cartesian product of sets What is a Cartesian product? Does it have anything to do with ordered pairs? How do we find the number of elements? And does order of multiplication matter? We'll cover all of this in this video. We'll also solve a few example problems to strengthen our concepts for this topic. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Cartesian product of sets What is a Cartesian product? Does it have anything to do with ordered pairs? How do we find the number of elements? And does order of multiplication matter? We'll cover all of this in this video. We'll also solve a few example problems to strengthen our concepts for this topic. https://cdn.kastatic.org/ka-youtube-converted/pggK5QOzc7w.mp4/pggK5QOzc7w.mp4 386 Cartesian product of sets https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1219/v/ordered-triplets 2025-03-01T15:52:37.13987578Z Ordered triplets We've discussed what ordered pairs are. In this video, we'll expand that idea to triplets. We'll learn how to find the cartesian product of three sets. We'll also look at the geometrical significance of double and triple products of R. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Ordered triplets We've discussed what ordered pairs are. In this video, we'll expand that idea to triplets. We'll learn how to find the cartesian product of three sets. We'll also look at the geometrical significance of double and triple products of R. https://cdn.kastatic.org/ka-youtube-converted/ONsTL2Npt24.mp4/ONsTL2Npt24.mp4 317 Cartesian product of sets https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1219/v/cartesian-product-axb-given 2025-03-01T15:52:37.13987578Z Cartesian product (AxB given) In this worked example, we're given AxB and we need to figure out A and B. We'll leverage the key principle of ordered pairs here - that the elements of the cartesian product pick elements from individual sets in order. For AxB, first elements will always be picked from A and the second elements will always be picked from B. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Cartesian product (AxB given) In this worked example, we're given AxB and we need to figure out A and B. We'll leverage the key principle of ordered pairs here - that the elements of the cartesian product pick elements from individual sets in order. For AxB, first elements will always be picked from A and the second elements will always be picked from B. https://cdn.kastatic.org/ka-youtube-converted/jIy-K54uqhg.mp4/jIy-K54uqhg.mp4 198 Cartesian product of sets https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1219/v/cartesian-product-set-operations 2025-03-01T15:52:37.13987578Z Cartesian product (Set operations) In this worked example, we solve a problem involving set operations of cartesian product of sets. We first find intersection and union of sets and then find intersection and union of cross product of sets. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Cartesian product (Set operations) In this worked example, we solve a problem involving set operations of cartesian product of sets. We first find intersection and union of sets and then find intersection and union of cross product of sets. https://cdn.kastatic.org/ka-youtube-converted/woPMZkMyVVI.mp4/woPMZkMyVVI.mp4 231 Cartesian product of sets https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1219/v/cartesian-product-application-based 2025-03-01T15:52:37.13987578Z Cartesian Product (Application based) In this video, we're playing the role of a detective and using our knowledge of cartesian products to determine what's missing. We'll leverage the key principle: Cartesian product has elements that are ordered pairs. The first element is always picked from the first set and the second element is always picked from the second set. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Cartesian Product (Application based) In this video, we're playing the role of a detective and using our knowledge of cartesian products to determine what's missing. We'll leverage the key principle: Cartesian product has elements that are ordered pairs. The first element is always picked from the first set and the second element is always picked from the second set. https://cdn.kastatic.org/ka-youtube-converted/hcojmHZQcAA.mp4/hcojmHZQcAA.mp4 196 Cartesian product of sets https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1219/e/cartesian-product-of-sets 2026-02-26T15:40:49.311158104Z Cartesian product of sets Covers CP of two sets. exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1219/e/identify-sets-from-cartesian-product 2025-02-27T11:46:16.621461116Z Identify sets from cartesian product Information about AxB is given. Find set A/B. exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:untitled-1219/e/worked-example-cartesian-product 2025-05-22T15:13:46.85517145Z Worked example - Cartesian product Worked example - Cartesian product (application based) Ashish Gupta exercise