Question

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

• A. $\alpha=14$
• B. $\alpha$ is a multiple of 4
• C. 4 is the remainder when $\alpha$ is divided by 10
• D. 4 is the remainder when $\alpha$ is divided by 7

Answer 1

Answer: (D)

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

Answer 2

From the given options the correct answer is option (D): 4 is the remainder when $\alpha$ is divided by 7