Let $R =\{( P , Q ) \mid P$ and $Q$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of $(1,-1)$ is the set
$S =\left\{( x , y ) \mid x ^{2}+ y ^{2}=4\right\}$
$S =\left\{( x , y ) \mid x ^{2}+ y ^{2}=1\right\}$
$S =\left\{( x , y ) \mid x ^{2}+ y ^{2}=\sqrt{2}\right\}$
$S=\left\{(x, y) \mid x^{2}+y^{2}=2\right\}$
Maximum number of equivalence relations on set $A = \{1, 2, 3, 4\}$ is $N$, then -
If $R$ is an equivalence relation on a set $A$, then ${R^{ - 1}}$ is
$R$ is a relation from $\{11, 12, 13\}$ to $\{8, 10, 12\}$ defined by $y = x - 3$. Then ${R^{ - 1}}$ is
Let $S$ be the set of all real numbers. Then the relation $R = \{(a, b) : 1 + ab > 0\}$ on $S$ is
Let $R$ and $S$ be two equivalence relations on a set $A$. Then