For α N, consider a relation R on N given by R=\(x, y): 3 x+α y is a multiple of 7. The relation R is an equivalence relation if and only if:

(D) 4 is the remainder when α is divided by 7

(C) 4 is the remainder when α is divided by 10

Sets, Relations and Functions: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jul, Morning shift · Q5383

JEE Main 202228 Jul, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

For

\alpha \in \mathbf{N}

, consider a relation

\mathrm{R}

\mathbf{N}

given by

\mathrm{R}=\{(x, y): 3 x+\alpha y

is a multiple of 7

\}

. The relation

R

is an equivalence relation if and only if :