Q1.2

MCQ1 mark, −0.25

Consider the following relations: $R_1\:(a,b)$ iff $(a+b)$ is even over the set of integers $R_2 \:(a,b)$ iff $(a+b)$ is odd over the set of integers $R_3 \:(a,b)$ iff $a.b > 0$ over the set of non-zero rational numbers $R_4\:(a,b)$ iff $|a-b| \leq 2$ over the set of natural numbers Which of the following statements is correct?

(A)

$R_1$ and $R_2$ are equivalence relations, $R_3$ and $R_4$ are not

(B)

$R_1$ and $R_3$ are equivalence relations, $R_2$ and $R_4$ are not

(C)

$R_1$ and $R_4$ are equivalence relations, $R_2$ and $R_3$ are not

(D)

$R_1, R_2, R_3$ and $R_4$ all are equivalence relations

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