$\text { If } A=\{1,2,3,4,5\} \text { and } B=\{2,3,6,7\} \text { then number of elements in the set }(A \times B) \cap(B \times A) \text { is equal to }$

The set $A \times B$ consists of all ordered pairs $(a, b)$ where $a \in A$ and $b \in B$.

The set $B \times A$ consists of all ordered pairs $(b, a)$ where $b \in B$ and $a \in A$.

An element $(x, y)$ belongs to $(A \times B) \cap (B \times A)$ if and only if $(x, y) \in A \times B$ and $(x, y) \in B \times A$.

This implies $x \in A$, $y \in B$, $x \in B$, and $y \in A$.

Therefore, $x \in A \cap B$ and $y \in A \cap B$.

Given $A = \{1, 2, 3, 4, 5\}$ and $B = \{2, 3, 6, 7\}$, the intersection $A \cap B = \{2, 3\}$.

The number of elements in $A \cap B$ is $n(A \cap B) = 2$.

The set $(A \times B) \cap (B \times A)$ is equivalent to $(A \cap B) \times (A \cap B)$.

The number of elements is $n((A \cap B) \times (A \cap B)) = n(A \cap B) \times n(A \cap B) = 2 \times 2 = 4$.

Answer: 4