Let n(A) denotes the number of elements in the set A. If nA=4, nB=5 and nA∩B=3, then n[(A×B)∩(B×A)] is equal to

Correct answer: (B) 9. Given, nA=4, nB=5 and nA∩B=3 ∴nA×B∩B×A=nA∩B×B∩A=3^2=9

Q24 / 35 · NTA Abhyas (JEE Main) 2020 · Mathematics · Sets and Relations

Let $n (A)$ denotes the number of elements in the set $A$ . If $n (A) = 4, n (B) = 5$ and $n (A \cap B) = 3$ , then $n [(A \times B) \cap (B \times A)]$ is equal to

Given,

n (A) = 4, n (B) = 5

and

n (A \cap B) = 3

∴ n [(A \times B) \cap (B \times A)] = n [(A \cap B) \times (B \cap A)] = 3^{2} = 9

Hence, the correct answer is option: 'B'.