Number of subsets of a set

Number of subsets of a set = 2 ⁿ

where n is the number of elements of the set

For set A = {1, 2}

The subsets are ∅, {1}, {2}, {1, 2}

So, Number of subsets = 2 ² = 4

Similarly,

For B = {1, 2, 3}

Subsets will be

∅,

{1}, {2}, {3},

{1, 2}, {2, 3}, {1, 3},

{1, 2, 3}

So, Number of subsets = 2 ³ = 8

Number of elements of power set

Now,

We know that power set is the set of all subsets.

∴ Number of elements of power set = Number of subsets of set 

Number of elements of power set = 2 ⁿ