Let R be a relation on the set N be defined by ${(x, y) | x, y ϵ N, 2 x + y = 41}$ . Then R is

Reflexive

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Symmetric

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Transitive

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None of these

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Solution

The correct option is D None of these
On the set N of natural numbers,
$R = {(x, y); x, y ϵ N, 2 x + y = 41} .$
Since $(1, 1) / ϵ R$ as $2.1 + 1 = 3 \neq 41$ . So, R is not reflexive. Where R is the Relation.
$(1, 39) ϵ R b u t (39, 1) / ϵ R$ . So R is not symmetric (20, 1)
$(1, 39) ϵ R$ . But $(20, 39) / ϵ R$ , So R is not transitive.

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