The relation R in the set of natural numbers N defined as R = { ( x , y ) : y = x + 5 and x 4 } is:

Question

The relation $R$ in the set of natural numbers $N$ defined as $R = {(x, y) : y = x + 5 and x < 4}$ is:

Smart Achievers · Accepted Answer

(4)

Ans. None of these

Explanation:

$R = {(1, 6), (2, 7), (3, 8)}$

$∵$ $(6, 6) \notin R$

$\Rightarrow R is not reflexive.$

For $(2, 7) \in R$

$\Rightarrow$ $(2, 7) \in R but (7, 2) \notin R$

$\Rightarrow R is not symmetric.$

Clearly, $R$ is not transitive.

(Since, there is no pair in $R$ such that $(x, y)$ and $(y, z) \in R$ , then $(x, z) \in R$ )

$\Rightarrow$ R is not an equivalence relation.

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