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If two sets A and B are having 43 elements in comman, then the number of elements common to each of the sets A x B and B x A is

(a) 432 

(b) 243 

(c) 4343 

(d) 286

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The correct option (a) 432

Explanation:

n((A x B) ∩ (B x A)) = n((A ∩ B) x (B ∩ A)) 

= n(A ∩ B) . n(B ∩ A) 

= 43 x 43 = 432

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