The relation "congruence modulo $m$" is
Reflexive only
Transitive only
Symmetric only
An equivalence relation
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
The void relation on a set $A$ is
In the set $A = \{1, 2, 3, 4, 5\}$, a relation $R$ is defined by $R = \{(x, y)| x, y$ $ \in A$ and $x < y\}$. 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?
The relation $R =\{( a , b ): \operatorname{gcd}( a , b )=1,2 a \neq b , a , b \in Z \}$ is: