Question

The relation S = { (3,3) (4,4) } on the set A =  {3,4,5} is

A. Not reflexive but symmetric and transitive

B. Reflexive only

C. Symmetric only

D. An equivalence relation

Answer 1

Hint: Let’s consider elements of a set as a,b and c and go with the definition of reflexive, symmetric and transitive.

Complete step by step answer:

As given that set is A = 3,4,5} and the relation is S =  { (3,3) (4,4) }

And as we know the relation above will not be reflexive because every element of A is not related to itself as  (5,5) is absent.

But A is symmetric because if for all a and b in A that a is related to b if and only if b is related to a.

And also A is transitive because if a is related to b and b is related to c then a is also related to c.

Hence we can conclude that the given relation is not reflexive but symmetric and transitive.

So, the correct option is A.

Note: Whenever you come up with this type of problem where it is asked about relation with set, a better knowledge of definitions will be an added advantage.