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For a pair (A,B) of subsets of the set X=(1,2,...100), let A*B denote the set of all elements of X which belong to exactly one of A or B. what is number of pairs (A,B) of subsets of X such that A*B=(2,4,6,...100)?
I let A =(1,2,3...50) and B=(51,52,...100) so there are 25 elememnts of even numbers in each set, multiply them, so there are 625 pairs of (A,B).
I let A =(1,2,3...50) and B=(51,52,...100) so there are 25 elememnts of even numbers in each set, multiply them, so there are 625 pairs of (A,B).