For $\alpha \in \mathbf{N}$, consider a relation $\mathrm{R}$ on $\mathbf{N}$ 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 :

Question

$\alpha=14$

$\alpha$ is a multiple of 4

4 is the remainder when $\alpha$ is divided by 10

4 is the remainder when $\alpha$ is divided by 7

Solution

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