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Cartesian Product of sets (Part - 2) - Concepts, Math, Class 11 Video Lecture

FAQs on Cartesian Product of sets (Part - 2) - Concepts, Math, Class 11 Video Lecture

1. What is the Cartesian product of sets?
Ans. The Cartesian product of two sets A and B, denoted by A x B, is the set of all ordered pairs (a, b) where a belongs to A and b belongs to B. In other words, it is the set of all possible combinations of elements from A and B.
2. How do you calculate the size of the Cartesian product of two sets?
Ans. The size of the Cartesian product of two sets A and B is equal to the product of the number of elements in A and the number of elements in B. Mathematically, if |A| represents the number of elements in A and |B| represents the number of elements in B, then the size of A x B is |A| * |B|.
3. Can the Cartesian product of two sets be empty?
Ans. Yes, the Cartesian product of two sets can be empty. This happens when at least one of the sets is empty. If either set A or set B is empty, then the Cartesian product A x B will also be empty.
4. What is the difference between the Cartesian product and the intersection of sets?
Ans. The Cartesian product of two sets A and B produces a set of ordered pairs, whereas the intersection of two sets A and B produces a set of common elements between the two sets. In other words, the Cartesian product focuses on combining elements from two sets, while the intersection focuses on finding common elements.
5. Can the Cartesian product of two sets contain duplicate elements?
Ans. No, the Cartesian product of two sets does not contain duplicate elements. Each element in the Cartesian product is unique and represents a distinct combination of elements from the two sets. If there are duplicate elements in either set, they will only appear once in the Cartesian product.
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