Proper Set
A is said to be a proper subset of B if:
- A is a subset of B
- A is not equal to B
- A is a subset of B but B contains at least one element which does not belong to A
Improper Set
Sct A is called an improper subset of B if and only if A = B. Every set is an improper subset of itself.
Power Set
The power set of a set is defined as a set of every possible subset if the cardinality of A is ‘n’ then the cardinality of power set is 2n as every element has two options either t0 belong t0 a subset or not
Finite Set
This is a set consisting of natural number of objects. If the members of a set have definite numbers like the days of the week, we term this as finite
Consider the sets
A = { 5, 7, 9, 11 }
B = {4, 8, 16, 32} are both finite set
Infinite Set
If the number of elements in a set is infinite, the set is said to be infinite.
Thus the set of all natural numbers is given by N = {1.2.3,.} is an infinite set. Similarly the set of all rational numbers between 0 and 1 given by
A = {x:x £ Q, 0<x<1} is an infinite set