Power Set
Power set
Let A be a set. Then the collection or family of all subsets of A is called the power set of A and is denoted by P(A).
That is. P(A) = { S : S ⊂ A }.
Since the empty set and the set A itself are subsets of A and are therefore elements of P(A).Thus, the power set of a given set is always non-empty.
Example
Let A ={1, 2, 3 } Then, the subsets of A are : , Φ {1},{2},{3},{1, 2},{1, 3},{2, 3} and {1, 2, 3}. Hence, P(A) = {Φ, {1},{2},{3},{1, 2},{1, 3},{2, 3},{1, 2, 3}}.
Example
if A is the void set , then P(A) has just one element P(Φ) = {Φ}.
Example
REMARK
We know that a set having n elements has 2n subsets. Therefore, if A is a finite set having n elements, then P(A) has 2n elements.