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Let the sets be A, B, C, D then (A ∩ B) X (C ∩ D) is equivalent to __________

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Let the sets be A, B, C, D then  (A ∩ B) X (C ∩ D) is equivalent to __________

(a) (A X C) ∩ (B X D)

(b) (A X D) U (B X C)

(c) (A X C) U ( B X D)

(d) None of the mentioned

The question was asked during an internship interview.

This interesting question is from Cartesian Product of Sets topic in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

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Correct option is (a) (A X C) ∩ (B X D)

Easiest explanation: (A ∩ B) X (C ∩ D) = (A X C) ∩ (B X D) but in case of unions this is not true.

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