IIT JEE , AIEEE Forum - Mathematics , Algebra

Avinash_Bhat

REFLEXIVE RELATION : A relation R on a set A is reflexive if: (a,a) R for all 'a' A.

Eg : A = {1, 2}, then R = { (1,1) , (2,2) , (1,2) } is a reflexive relation on A.

TRANSITIVE RELATION : A relation R on a set A is transitive if : (a,b) R and (b,c) R => (a,c) R for all a,b,c R.

Eg : A = {1, 2, 3}, then R = { (1,2) , (2,3), (1,3) } is a transitive relation on A.

SYMMETRIC RELATION : A relation R on a set A is symmetric if : (a,b) R => (b,a) R for all a,b A.

Eg : A = {1, 2}, then R = { (1,2) , (2,1) } is a symmetric relation on A.

EQUIVALENCE RELATION : A relation R on a set A is reflexive, transitive and symmetric; then it is an equivalence relation.

Eg : A = {1, 2, 3}, then R = { (1,1) , (2,2) , (3,3) , (1,2) , (2,3) , (1,3) , (3,1) , (2,1) , (3,2) } is an equivalence relation on A.

I really can't put down anything , simpler than this ...........