Sets

10. Power Set

The family of all the subsets of any set S is called the power set of S.

We denote the power set of S by: 2S

Example 11.1: Let M = {a,b} Then 2

M = {{a, b}, {a}, {b}, ∅}

Example 11.2: Let T = {4,7,8} then 2

T = {T, {4,7}, {4,8}, {7,8}, {4}, {7},

{8}, ∅}

If a set S is finite, say S has n elements, then the power set of S can be shown to have 2n elements. This is one reason why the class of subsets of S is called

the power set of S and is denoted by 2 S.