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
$S =\left\{( x , y ) \mid x ^{2}+ y ^{2}=4\right\}$
$S =\left\{( x , y ) \mid x ^{2}+ y ^{2}=1\right\}$
$S =\left\{( x , y ) \mid x ^{2}+ y ^{2}=\sqrt{2}\right\}$
$S=\left\{(x, y) \mid x^{2}+y^{2}=2\right\}$
If $R$ be a relation $<$ from $A = \{1,2, 3, 4\}$ to $B = \{1, 3, 5\}$ i.e., $(a,\,b) \in R \Leftrightarrow a < b,$ then $Ro{R^{ - 1}}$ is
Let $R_1$ be a relation defined by $R_1 =\{(a, b) | a \geq b, a, b \in R\}$ . Then $R_1$ is
Let $R$ be a relation defined on $N$ as a $R$ b is $2 a+3 b$ is a multiple of $5, a, b \in N$. Then $R$ is
Let $R$ be a relation on the set $N$ of natural numbers defined by $nRm $$\Leftrightarrow$ $n$ is a factor of $m$ (i.e.,$ n|m$). Then $R$ is
Define a relation $R$ over a class of $n \times n$ real matrices $A$ and $B$ as $"ARB$ iff there exists a non-singular matrix $P$ such that $PAP ^{-1}= B "$ Then which of the following is true?