__SUBSET:__**A set P is said to be a subset of a set Q if each element of P is also an element of Q.** If P is subset of Q, we write

__PROPER SUBSET:__ If and then P is called a proper subset of Q and we write

**Example**: Consider and

Here, but

Every element of P lies in Q, but every element of Q does not lies in P.

If and

__SOME IMPORTANT PROPERTIES OF SUBSETS__

(1)

Where N = Natural number

Z = Integers

Q = Rational Numbers

R = Real Numbers

C = Complex Numbers

(2) Every set is its own subset.

(3) The empty set is subset of every set.

(4) The total number of subsets of a finite set containing n element is

__POWER SET:__**The set of all subsets of a given set A is called the power set of A, denoted by **. Example:

Subsets of A are:

__UNIVERSAL SET:__**A set that contains all set in a given context is called the universal set. It is denoted by U.**

Let and and

We can consider U as

Here,