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
Every element of P lies in Q, but every element of Q does not lies in P.
SOME IMPORTANT PROPERTIES OF SUBSETS
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