View source for Problem: Find (A ∩ B) × (B ∩ C)

= Problem: Find (A ∩ B) × (B ∩ C) =

Given sets:  
<math>A = \{3, 5, 7\}</math>  
<math>B = \{7, 8\}</math>  
<math>C = \{8, 9\}</math>  

== 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:  
<math>A \cap B = \{7\}</math>  

== Step 2: Find the Intersection B ∩ C ==

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

Common element is:  
<math>B \cap C = \{8\}</math>  

== 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:  
<math>A \cap B = \{7\}</math>  
<math>B \cap C = \{8\}</math>  

The Cartesian product is:  
<math>(A \cap B) \times (B \cap C) = \{ (7, 8) \}</math>  

== Final Answer ==

<math>(A \cap B) \times (B \cap C) = \{ (7, 8) \}</math>  

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### 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)