mathematic I Let A 14 15 16 17 18 19 How many subsets does

Let A = {14, 15, 16, 17, 18, 19}. How many subsets does A have? How many proper subsets does A have? A has subsets (Type a whole number)

Solution

a) The general formula of finding the number of subsets of a set containing n elements is 2^n

So, Here A = {14, 15, 16, 17, 18, 19}

n = 6

Number of subsets = 2^6 = 64

b) Any set is a subset of itself, but not a proper subset. (X X is true, and X X is false for any set X.) The empty set { }, denoted by , is also a subset of any given set X. It is also always a proper subset of any set except itself.

So, If a set contains ‘n’ elements, then the number of proper subsets of the set is 2^n - 1

Here, number of proper subsets = 2^6 - 1 = 64-1 = 63