https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:set-theory/x09646558c1ff0797:relations/v/what-are-ordered-pairs 2025-03-24T05:52:22.847271672Z क्रमित युग्म क्या होते हैं? (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 क्रमित युग्म क्या होते हैं? (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/UXx4P8PXO9M.mp4/UXx4P8PXO9M.mp4 268 समुच्चयों का कार्तीय गुणन (Cartesian product of sets) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:set-theory/x09646558c1ff0797:relations/v/cartesian-product-of-sets 2025-03-24T05:52:22.847271672Z समुच्चयों का कार्तीय गुणन (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 समुच्चयों का कार्तीय गुणन (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/giZ3OQvu8GA.mp4/giZ3OQvu8GA.mp4 386 समुच्चयों का कार्तीय गुणन (Cartesian product of sets) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:relations-and-functions-ncert-new/x808831787a7b08a2:untitled-1219/v/ordered-triplets 2025-03-24T05:52:22.847271672Z क्रमित त्रिक (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 क्रमित त्रिक (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/SRmn8xy8Ljs.mp4/SRmn8xy8Ljs.mp4 317 समुच्चयों का कार्तीय गुणन (Cartesian product of sets) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:relations-and-functions-ncert-new/x808831787a7b08a2:untitled-1219/v/cartesian-product-axb-given 2025-03-24T05:52:22.847271672Z कार्तीय गुणन (AxB दिया गया है) (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 कार्तीय गुणन (AxB दिया गया है) (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/IMriGLSPFTk.mp4/IMriGLSPFTk.mp4 198 समुच्चयों का कार्तीय गुणन (Cartesian product of sets) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:relations-and-functions-ncert-new/x808831787a7b08a2:untitled-1219/v/cartesian-product-set-operations 2025-03-24T05:52:22.847271672Z कार्तीय गुणन (समुच्चय संक्रियाएँ) (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 कार्तीय गुणन (समुच्चय संक्रियाएँ) (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/gehMydJW5fE.mp4/gehMydJW5fE.mp4 231 समुच्चयों का कार्तीय गुणन (Cartesian product of sets) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:relations-and-functions-ncert-new/x808831787a7b08a2:untitled-1219/v/cartesian-product-application-based 2025-03-24T05:52:22.847271672Z कार्तीय गुणन (अनुप्रयोग आधारित) (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 कार्तीय गुणन (अनुप्रयोग आधारित) (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/b8nu0QVOK8Q.mp4/b8nu0QVOK8Q.mp4 196 समुच्चयों का कार्तीय गुणन (Cartesian product of sets) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:relations-and-functions-ncert-new/x808831787a7b08a2:untitled-1219/e/cartesian-product-of-sets 2025-03-24T05:52:22.847271672Z समुच्चयों का कार्तीय गुणन (Cartesian product of sets) यहां दो समुच्चयों के कार्तीय गुणन से संबंधित प्रश्न शामिल किए गए हैं| exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:relations-and-functions-ncert-new/x808831787a7b08a2:untitled-1219/e/identify-sets-from-cartesian-product 2025-03-24T05:52:22.847271672Z कार्तीय गुणन (cartesian product) से समुच्चयों को पहचानना AxB की जानकारी दी गई है। समुच्चय A/B ज्ञात करें। exercise