Question

In a set of teachers of a school, two teachers are said to be related if they teach the same subject, then the relation is (Assume that every teacher teach only one subject)

• A. Reflexive and symmetric
• B. Symmetric and transitive
• C. Reflexive and transitive
• D. Equivalence

Answer 1

Answer: (A)

Reflexive and symmetric

Let R be the relation give in the question

Let A be any teacher

then $\left(A,A\right)\in R$

since A and A is the same teacher

so, it is reflexive

Suppose

$\left(A,B\right)\in R$

A and B teach same subject

B and A teach same subject

$\left(B,A\right)\in R$

R is symmetric

But

$\left(A,B\right)\in R\ne \left(B,C\right)\in R$

so, it is not transitive

therefore R is reflexive and symmetric