#### Question

If *A* = {*a*, *b*, *c*}, then the relation *R* = {(*b*, *c*)} on *A* is

(a) reflexive only

(b) symmetric only

(c) transitive only

(d) reflexive and transitive only

#### Solution

(c) transitive only

The relation *R* = {(b,c)} is neither reflexive nor symmetric because every element of *A* is not related to itself. Also, the ordered pair of *R* obtained by interchanging its elements is not contained in *R*.

We observe that* R *is transitive on *A *because there is only one pair.

Is there an error in this question or solution?

Solution If a = {A, B, C}, Then the Relation R = {(B, C)} on a is (A) Reflexive Only (B) Symmetric Only (C) Transitive Only (D) Reflexive and Transitive Only Concept: Types of Relations.