Sets and Functions

Important formulae on sets

1. Number of subsets of a set of n elements is 2n

2. Number of proper subsets of a set of n elements is 2n-1

3. If A and B are two non-empty set, in which number of elements are m and n respectively, then ....

(a) Number of elements in A×B=mn

(b) Number of relations from A to B=2mn

(c) Number of functions from A to B =nm

4. If A is a non-empty set in which number of elements is n, then....

(a) Number of elements in A×A=n2

(b) Number of relations from A to A= 2nxn

(c) Number of functions from A to A= nn

(d) If f is a function then Domain of f= range of f-1 and domain of f-1= range of f

You check your answers by using these formulae.

Sujatha Raghavan,
Math teacher.