Let $R$ be a relation over the set $N × N$ and it is defined by $(a,\,b)R(c,\,d) \Rightarrow a + d = b + c.$ Then $R$ is
Reflexive only
Symmetric only
Transitive only
An equivalence relation
The void relation on a set $A$ 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.
The relation $R= \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$ on set $A = \{1, 2, 3\}$ is
Solution set of $x \equiv 3$ (mod $7$), $p \in Z,$ is given by
Show that the relation $R$ in $R$ defined as $R =\{(a, b): a \leq b\},$ is reflexive and transitive but not symmetric.