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 = 2ⁿ - 1

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

⇒2ⁿ = 32

⇒2ⁿ = 2⁵

⇒n = 5 

Hence,the number of elements of A is 5.