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Symmetric Relations

In the set ...

Question

In the set $A = {1, 2, 3, 4, 5}$ , a relation $R$ is defined by $R = {(x, y) | x, y \in A a n d x < y}$ . Then $R$ is

A

Reflexive

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B

Symmetric

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C

Transitive

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D

None of these

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Solution

The correct option is B Transitive
Since $x ≮ x$ , therefore $R$ is not reflexive. Also $x < y$
does not imply that $y < x$ , So $R$ is not symmetric. Let $x R y$
and $y R z$ . Then $x < y$ and $y < z \Rightarrow x < z$ i.e.,
$x R z$ . hence $R$ is trasitive.

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