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# 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 - CBSE (Arts) Class 12 - Mathematics

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#### Question

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

• reflexive only

• symmetric only

• transitive only

• reflexive and transitive only

#### Solution

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?

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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.
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