Let A = {1, 2, 3, 4, 5} and B = {2, 3, 6, 7}. | vedclass

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(C) The Cartesian product $A 	imes B$ consists of all ordered pairs $(a, b)$ where $a \in A$ and $b \in B$.Similarly,$B 	imes A$ consists of all ord

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$4$

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(C) The Cartesian product $A 	imes B$ consists of all ordered pairs $(a, b)$ where $a \in A$ and $b \in B$.Similarly,$B 	imes A$ consists of all ordered pairs $(b, a)$ where $b \in B$ and $a \in A$.The intersection $(A 	imes B) \cap (B 	imes A)$ contains all ordered pairs $(x, y)$ such that $(x, y) \in A 	imes B$ and $(x, y) \in B 	imes A$.This implies $x \in A, y \in B$ and $x \in B, y \in A$.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 number of elements in $(A 	imes B) \cap (B 	imes A)$ is $n(A \cap B) 	imes n(A \cap B) = 2 	imes 2 = 4$.The elements are $(2, 2), (2, 3), (3, 2), (3, 3)$.

Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{2, 3, 6, 7\}$. Then the number of elements in $(A \times B) \cap (B \times A)$ is:

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