Question

Let $A=\{1,2,3,4\}$ and $B=\{7,8,3,4\}$. Then the number of elements common to both $A \times B$ and $B \times A$ is ________.

• A. 8
• B. 6
• C. 12
• D. 4
• E. 2

Hint:

$n((A \times B) \cap (B \times A)) = (n(A \cap B))^2$.

Answer 1

The Correct Option is D

Step 1: Concept
The number of elements common to $A \times B$ and $B \times A$ is $(n(A \cap B))^2$.

Step 2: Meaning
Find the intersection of sets $A$ and $B$.

Step 3: Analysis
$A \cap B = \{3, 4\}$. The number of common elements $n(A \cap B) = 2$.

Step 4: Conclusion
Number of common elements in products $= 2^2 = 4$. Final Answer: (D)