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UGC NET Computer Science Dec 2022 Shift I (Paper II)

The relation


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


defined in ${1,2,3,4}$ is ____

Solution

For reflexive relation, $(1,1),(2,2),(3,3),(4,4)$ must be present.

But $(2,2)$ is missing.

So, relation is not reflexive.

For symmetric relation, if $(1,2)$ is present, then $(2,1)$ must also be present.

But $(2,1)$ is missing.

So, relation is not symmetric.

For transitive relation, since $(3,1)$ and $(1,2)$ are present, then $(3,2)$ must be present.

But $(3,2)$ is missing.

So, relation is not transitive.

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