The relation "congruence modulo $m$" is
Reflexive only
Transitive only
Symmetric only
An equivalence relation
Let $R\,= \{(x,y) : x,y \in N\, and\, x^2 -4xy +3y^2\, =0\}$, where $N$ is the set of all natural numbers. Then the relation $R$ is
Let $N$ be the set of natural numbers and a relation $R$ on $N$ be defined by $R=\left\{(x, y) \in N \times N: x^{3}-3 x^{2} y-x y^{2}+3 y^{3}=0\right\} .$ Then the relation $R$ is:
Show that the relation $R$ in the set $A$ of all the books in a library of a college, given by $R =\{(x, y): x $ and $y$ have same number of pages $\}$ is an equivalence relation.
Let $R$ be a relation on a set $A$ such that $R = {R^{ - 1}}$, then $R$ is
Show that the relation $R$ in the set $\{1,2,3\}$ given by $R =\{(1,2),(2,1)\}$ is symmetric but neither reflexive nor transitive.