How many subsets can be made from a set of six elements, including the null set and the set itself?
(i) 84(ii) 64(iii) 32

Solution:

Option (ii) is the correct answer.

If the set has ‘n’ elements then, the number of subsets of it is given by 2ⁿ. Now, the given set has 6 elements.

Therefore, number of subsets =2⁶ = 64

This includes all the subsets including the null set and set itself.

Note: Suppose the question was, the number of subsets excluding the null set and itself then, the number of subsets possible will be equal to 2ⁿ- 2 = 62.

How many subsets can be made from a set of six elements, including the null set and the set itself?
(i) 84(ii) 64(iii) 32

Summary:

The subsets that can be made from a set of six elements, including the null set and the set itself, are 64.