Let $A =\{1,2,3,4,5,6,7\}$. Then the relation $R =$ $\{( x , y ) \in A \times A : x + y =7\}$ is
transitive but neither symmetric nor reflexive
reflexive but neither symmetric nor transitive
an equivalence relation
symmetric but neither reflexive nor transitive
Given the relation $R = \{(1, 2), (2, 3)\}$ on the set $A = {1, 2, 3}$, the minimum number of ordered pairs which when added to $R$ make it an equivalence relation is
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
If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements, then the number of relations from $A$ to $B$ is
Check whether the relation $R$ defined in the set $\{1,2,3,4,5,6\}$ as $R =\{(a, b): b=a+1\}$ is reflexive, symmetric or transitive.
Let $R$ be a relation on a set $A$ such that $R = {R^{ - 1}}$, then $R$ is