What is power set?

POWER SET Definition: The power set of a set A is the set of all the subsets of A, and is denoted by P(A).

Basic Combinatorics

Mathematically, P(A) = { x:x ⊆ A}.

Note that Ø ∈P(A) and A ∈ P(A) for all sets A. For example, if A={1}, then P(A)= {Ø ,{1}} and if A= {1,2}, then P(A)={Ø, {1}, {2}, {1,2}}

Similarly, if A = {1,2,3}, then P(A) = {Ø ,{1}, {2}, {3}, {1,2}, {1,3}, {2,3},

{1,2,3}}.

Definition: Any set which is a superset of all the sets under consideration is known as the universal set. This is usually denoted by Ω , S or U.

For example, if A = {1,2,3}, B = {3,4,6,9} and C = {0,1}, then we can take U = {0,1,2,3,4,5,6,7,8,9} or U= N, or U=as the universal set.

You may also like...

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

error: Content is protected !!