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)
Answer
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.
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.
