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If set A and B have 3 and 4 elements respectively then the number of subsets of set (A X B) is?

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If set A and B have 3 and 4 elements respectively then the number of subsets of set (A X B) is?

(a) 1024

(b) 2048

(c) 512

(d) 4096

This question was addressed to me in a national level competition.

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

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Correct option is (d) 4096

Easy explanation: The A X B has 12 elements, then the number of the subset are 2 12  = 4096.

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