jee-main 2022 Q69

jee-main · India · session2_28jul_shift1 Proof Proof of Equivalence or Logical Relationship Between Conditions

For $\alpha \in \mathbb{N}$, consider a relation $R$ on $\mathbb{N}$ given by $R = \{(x, y) : 3x + \alpha y \text{ is a multiple of } 7\}$. The relation $R$ is an equivalence relation if and only if
(1) $\alpha = 14$
(2) $\alpha$ is a multiple of 4
(3) 4 is the remainder when $\alpha$ is divided by 10
(4) 4 is the remainder when $\alpha$ is divided by 7

For $\alpha \in \mathbb{N}$, consider a relation $R$ on $\mathbb{N}$ given by $R = \{(x, y) : 3x + \alpha y \text{ is a multiple of } 7\}$. The relation $R$ is an equivalence relation if and only if\\
(1) $\alpha = 14$\\
(2) $\alpha$ is a multiple of 4\\
(3) 4 is the remainder when $\alpha$ is divided by 10\\
(4) 4 is the remainder when $\alpha$ is divided by 7

Paper Questions

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