Question

Using a Venn diagram find the number of a subset of a given set and verify that if a set has n number of elements, the total number of subsets is 2n​

Answer 1

Number of Subsets of a given Set:

If a set contains ‘n’ elements, then the number of subsets of the set is 22.

Number of Proper Subsets of the Set:

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

If A = {p, q} the proper subsets of A are [{ }, {p}, {q}]

⇒ Number of proper subsets of A are 3 = 22 - 1 = 4 - 1

In general, number of proper subsets of a given set = 2m - 1, where m is the number of elements.