For example ,
A = { All books of Algebra in your library }
B = { All books of Geometry in your library }
C = { All books in your library }
Here, the set C is taken as the universal set .
Complement of a set : Let È be the universal set and set A Ì B. The complement of the set A with respect to the universal set È is denoted by A˘ is defined as
A˘ or = { x  x ÎÈ but x Ï A }
For example
È = { 1, 2, 3, 4, . . . } and A = { 1, 3, 5, 7, . . . }
then A˘ = { 2, 4, 6, 8, . . . }
Equivalent sets : Two sets are equivalent if and
only if, a 1  1 correspondence exists between them.
For example
 If A = { 1, 2, 3 }, B = {a, b, c } then A and B are 11. equivalent, since the correspondence between them is
 If A = { x  x ÎN, x < 5} B = { x  x is a set of the word Dear }, then A and B are equivalent.
Note : If two sets are equal, then they must be equivalent. But two equivalent sets need not be equal.
Power set : The set of all subsets of a set A is the power set of the set A. It is denoted by p(A)
For example A = {1, 2}. The power set of A is p(A) = {{1}, {2}, {1,2}, { }}
Note : The number of elements are 2 and number of subsets are 4. Then 4 = 2^{2} Þ if there are 'n' number of elements in any set, the number of its subsets is given by 2^{n} .
Cardinal Number of a set : The cardinal number of a finite set 'A' is the number of elements of the set A. It is denoted by n (A).
For example, If A = { 1, 2, 3 } , B = {a, b, c} then n (A) = 3 and n (B) = 3.
Thus n (A) = n (B) but n (A) = n (B) does not imply that A = B. Also n (f ) = 0.
Difference between two set : The set of all elements belonging to a set A but not belonging to a set B. It is written as A  B.

Index
2.1 Sets 2.2
Operations on Sets 2.3
The Algebra of Sets
Chapter 3
