Relation R on real numbers is defined as R = {(a, b) : a b}.

Question

Relation R on real numbers is defined as $R = {(a, b) : a \leq b} .$

Smart Achievers · Accepted Answer

(3)

Ans. Reflexive and transitive but not symmetric

Explanation:

$R = {(a, b) : a \leq b}$

$(a, a) \in R$

$∵$ R is reflexive.

$(a, b), (b, c) \in R$

$a \leq b and b \leq c$

$a \leq c$

$(a, c) \in R$

Therefore, $R$ is transitive.

$(2, 4) \in R$

$(4, 2) \notin R$

Therefore $R$ is not symmetric.

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