Q1. show that relation R in the set A={1,2,3} given by R={(1,1),(2,2),(3,3),(1,2),(2,3)} is reflexive but neither symmetric nor transitive.

The relation R on set A = {1, 2, 3} is defined as  R = (1,1),(2,2),(3,3),(1,2),(2,3)}.

(1,1), (2,2), and (3,3) are the elements of R i.e. every element in A is related to itself.

 So, R is reflexive.

 

(1, 2) and (2, 3) are elements of R. R would be a symmetric relation if (2, 1) and (3, 2) would be the elements of R.

Since, (2, 1) and (3, 2) are not the elements of R so, R is not symmetric.

 

(1, 2) and (2, 3) are elements of R . R would a transitive relation, if (1,3) would be an elements of R.

Since, (1,3) is not an elements of R so, R is not transitive