Question

Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is (A) 1 (B) 2 (C) 3 (D) 4

Answer 1

Given set is A={ 1,2,3 }.

The reflexive relation of the given set is ( 1,1 ),( 2,2 ),( 3,3 ) and the symmetric relation is ( 1,2 ),( 1,3 )( 2,1 ),( 3,1 ). The relation is not transitive because ( 3,2 )∉R. The total number of possible pairs will be,

R={ ( 1,1 ),( 1,2 ),( 1,3 ),( 2,1 ),( 2,2 ),( 3,1 ),( 3,3 ) }.

For a relation which is reflexive and symmetric but not transitive, we do not consider that pair which is transitive in relation.

So, we do not add any two pairs ( 3,2 )and ( 2,3 )to relation because then Rbecomes transitive.

Thus, the total number of relation is one.

Therefore, option (A) is correct.