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:

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:

Smart Achievers · Accepted Answer

(1)

Ans. reflexive but not symmetric

Explanation:

Given that,

A = {1, 2, 3}

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

$∵$ (1, 1), (2, 2), (3, 3) $\in$ R

Hence, R is reflexive.

(1, 2) $\in$ R but (2, 1) $\notin$ R

Hence, R is not symmetric.

(1, 2) $\in$ R and (2, 3) $\in$ R

$\Rightarrow$ (1, 3) $\in$ R

Hence, R is transitive.

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