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

JEE Main 2022 Mathematics question

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

Answer: (D)

Reflexive: (a, a) R means is a multiple of 7 for every a N, so 7 | , i.e. ≡ −3 ≡ 4 (mod 7). Modulo 7 this gives ≡ 3x + 4y ≡ 3(x − y). Symmetric:

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Question ID VK-034783