Question

What is the difference between superset and power set of a set

Answer 1

Super Set: 

Whenever a set A is a subset of set B, we say the B is a superset of A and we write, B ⊇ A. 

Symbol ⊇ is used to denote ‘is a super set of’ 

For example;

A = {a, e, i, o, u} 

B = {a, b, c, ............., z}

Here A ⊆ B i.e., A is a subset of B but B ⊇ A i.e., B is a super set of A

Power Set: 

The collection of all subsets of set A is called the power set of A. It is denoted by P(A). In P(A), every element is a set. 

For example;

If A = {p, q} then all the subsets of A will be 

P(A) = {∅, {p}, {q}, {p, q}} 

Number of elements of P(A) = n[P(A)] = 4 = 22

In general, n[P(A)] = 2m where m is the number of elements in set A.