Q. 7

# For any two sets

We know,

(A × B) (B × A) = (A B) × (B A)

Here A and B have an element in common i.e., n(A B) = 1 = (B A)

So, n((A × B) (B × A)) = n((A B) × (B A)) = n(A B) × n(B A) = 1 × 1 = 1

That means, A × B and B × A have an element in common if and only if A and B have an element in common. [Proved]

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