Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer:

Question

Smart Achievers · Accepted Answer

(2)

Ans. R is reflexive and transitive but not symmetric.

Explanation:

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

It is seen that $(a, a) \in R$ , for every $a \in {1, 2, 3, 4}$

$∴$ R is reflexive.

It is seen that $(1, 2) \in R,$ but $(2, 1) \notin R$ .

$∴$ R is not symmetric.

Also, it is observed that $(a, b),$ $(b, c) \in R$ $\Rightarrow (a, c) \in R,$ for all $a, b, c \in {1, 2, 3, 4}$ .

$∴$ R is transitive.

Hence, R is reflexive and transitive but not symmetric.

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