If the number ofproper subsets of a set A is 31, find the number of elements of A.

Let the number of elements of set A = n.

Therefore, total number of proper subset = 2^{n} - 1

⇒2^{n} - 1 = 31 [Given, number of proper subset = 31]

⇒2^{n} = 32

⇒2^{n} = 2^{5}

⇒n = 5

Hence,the number of elements of A is 5.

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