Mark the correct alternative in the following question:

Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then, R is

(a) reflexive but not symmetric (b) reflexive but not transitive
(c) symmetric and transitive (d) neither symmetric nor transitive

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Solution

We have,

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

$As, (a, a) \in R \forall a \in A So, R is reflexive relation Also, (1, 2) \in R but (2, 1) \notin R So, R is not symmetric relation And, (1, 2) \in R, (2, 3) \in R and (1, 3) \in R So, R is transitive relation$

Hence, the correct alternative is option (a).

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