Problem

If $A=\{s, u\}$ and $B=\{v, w, x\}$, then complete the following. a. Find $A \times B$. b. Find $n(A \cap B)$. c. Write a multiplication equation involving numerals related to the answers in parts (a) and (b)

Solution

Step 1 :The Cartesian product of two sets A and B, denoted by A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. So, \(A \times B = \{(s, v), (s, w), (s, x), (u, v), (u, w), (u, x)\}\).

Step 2 :The intersection of two sets A and B, denoted by A ∩ B, is the set of all elements that are common to both A and B. Since there are no common elements in sets A and B, \(A \cap B = \emptyset\). Therefore, \(n(A \cap B) = 0\).

Step 3 :The multiplication equation involving numerals related to the answers in parts (a) and (b) is \(2 \times 3 = 6\), because there are 2 elements in set A and 3 elements in set B, and the Cartesian product of A and B has 6 elements.

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Source: https://solvelyapp.com/problems/fYRd38Poei/

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