A relation R on the set of natural numbers is | vedclass

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Question

(C) The relation $R$ is defined on the set of natural numbers $N$ as $R = \{(a, b) : a, b \in N, |a - b| = 3\}$.This means the difference between $a$

Vedclass · Accepted Answer

$\{(1, 4), (4, 1), (2, 5), (5, 2), (3, 6), (6, 3), \dots \}$

Vedclass · Answer

(C) The relation $R$ is defined on the set of natural numbers $N$ as $R = \{(a, b) : a, b \in N, |a - b| = 3\}$.This means the difference between $a$ and $b$ is $3$.If $b = 1$,then $|a - 1| = 3 \implies a = 4$ (since $a \in N$).If $b = 2$,then $|a - 2| = 3 \implies a = 5$.If $b = 3$,then $|a - 3| = 3 \implies a = 6$.If $a = 1$,then $|1 - b| = 3 \implies b = 4$.If $a = 2$,then $|2 - b| = 3 \implies b = 5$.Thus,the relation $R$ contains pairs such as $(1, 4), (4, 1), (2, 5), (5, 2), (3, 6), (6, 3), \dots$.Comparing this with the given options,option $C$ is the correct representation.

$A$ relation $R$ on the set of natural numbers is defined as $\{(a, b) : |a - b| = 3\}$. Then $R$ is:

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