Problem: Find (A ∩ B) × (B ∩ C)

Problem: Find (A ∩ B) × (B ∩ C)

Given sets: $A=\{3,5,7\}$ $B=\{7,8\}$ $C=\{8,9\}$

Step 1: Find the Intersection A ∩ B

Intersection means elements common to both sets.

Elements of A: 3, 5, 7 Elements of B: 7, 8

Common element is: $A\cap B=\{7\}$

Step 2: Find the Intersection B ∩ C

Elements of B: 7, 8 Elements of C: 8, 9

Common element is: $B\cap C=\{8\}$

Step 3: Find the Cartesian Product (A ∩ B) × (B ∩ C)

Cartesian product forms ordered pairs from every element of the first set with every element of the second set.

Since: $A\cap B=\{7\}$ $B\cap C=\{8\}$

The Cartesian product is: $(A\cap B)\times (B\cap C)=\{(7,8)\}$

Final Answer

$(A\cap B)\times (B\cap C)=\{(7,8)\}$

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1. 1. 1. Explanation:

- First, find elements common in both A and B → {7} - Then, find elements common in both B and C → {8} - Finally, create ordered pairs from these intersections → (7, 8)