Question

Which of the following relations is transitive but not reflexive for the set S={3, 4, 6}?

(a) R = {(3, 4), (4, 6), (3, 6)}

(b) R = {(1, 2), (1, 3), (1, 4)}

(c) R = {(3, 3), (4, 4), (6, 6)}

(d) R = {(3, 4), (4, 3)}

I had been asked this question by my college professor while I was bunking the class.

The origin of the question is Types of Relations topic in chapter Relations and Functions of Mathematics – Class 12

Answer 1

Right option is (a) R = {(3, 4), (4, 6), (3, 6)}

For explanation: For the above given set S = {3, 4, 6}, R = {(3, 4), (4, 6), (3, 6)} is transitive as (3,4)∈R and (4,6) ∈R and (3,6) also belongs to R . It is not a reflexive relation as it does not satisfy the condition (a,a)∈R, for every a∈A for a relation R in the set A.