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Let A = x N : x divides 36 and B = x N : x is a perfect square . Then the number of elements in the set C A : C B is ______

Correct answer

480

Step-by-step solution

The set A consists of all positive integer divisors of 36 . A = 1, 2, 3, 4, 6, 9, 12, 18, 36 The number of elements in A is n(A) = 9 . The set B consists of all perfect squares in natural numbers. The elements of A which are also in B are the perfect squares that divide 36 . A B = 1, 4, 9, 36 The elements of A which are not in B are: A B = 2, 3, 6, 12, 18 The number of elements in A B is 5 . The total number of subsets of A is 2^ n(A) = 2^9 = 512 . A subset C of A satisfies C B = if and only if C is formed entirely

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