QJEEM22Ma0c3b: JEE Main 2022 Mathematics - Class 11 JEEM22Ma0c3b Solution: Let R 1 = {(a, b) N N :

Question

Verified Solution • 2025–26 Session moderate

Let R₁ = {(a, b) $\in$ N $\times$ N : |a $-$ b| $\le$ 13} and

R₂ = {(a, b) $\in$ N $\times$ N : |a $-$ b| $\ne$ 13}. Then on N :

Accepted Answer

R_{1}=\{(a, b) \in N \times N:|a-b| \leq 13\}

and

R_{2}=\{(a, b) \in N \times N:|a-b| \neq 13\}

In

R_{1}: \because|2-11|=9 \leq 13

\therefore \quad(2,11) \in R_{1}

and

(11,19) \in R_{1}

but

(2,19) \notin R_{1}

\therefore \quad R_{1}

is not transitive

Hence

R_{1}

is not equivalence

In

R_{2}:(13,3) \in R_{2}

and

(3,26) \in R_{2}

but

(13,26) \notin R_{2}

(\because|13-26|=13)

\therefore R_{2}

is not transitive

Hence

R_{2}

is not equivalence.

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