Which one of the following relations on $R$ is an equivalence relation
$a\,{R_1}\,b \Leftrightarrow |a| = |b|$
$a{R_2}b \Leftrightarrow a \ge b$
$a{R_3}b \Leftrightarrow a \ {\rm{ divides }}\ b$
$a{R_4}b \Leftrightarrow a < b$
Consider the relations $R_1$ and $R_2$ defined as $a R_1 b$ $\Leftrightarrow a^2+b^2=1$ for all $a, b, \in R$ and $(a, b) R_2(c, d)$ $\Leftrightarrow a+d=b+c$ for all $(a, b),(c, d) \in N \times N$. Then
Let $n$ be a fixed positive integer. Define a relation $R$ on the set $Z$ of integers by, $aRb \Leftrightarrow n|a - b$|. Then $R$ is
Let $R$ and $S$ be two relations on a set $A$. Then
Let $R_1$ and $R_2$ be two relations on a set $A$ , then choose incorrect statement
If $R = \{ (x,\,y)|x,\,y \in Z,\,{x^2} + {y^2} \le 4\} $ is a relation in $Z$, then domain of $R$ is