The relation $R$ defined in $N$ as $aRb \Leftrightarrow b$ is divisible by $a$ is
Reflexive but not symmetric
Symmetric but not transitive
Symmetric and transitive
None of these
The relation $R= \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$ on set $A = \{1, 2, 3\}$ is
The number of relations, on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is
Show that the relation $R$ in the set $A=\{1,2,3,4,5\}$ given by $R =\{(a, b):|a-b|$ is even $\},$ is an equivalence relation. Show that all the elements of $\{1,3,5\}$ are related to each other and all the elements of $ \{2,4\}$ are
If $R$ is an equivalence relation on a Set $A$, then $R^{-1}$ is not :-
If $R = \{(6, 6), (9, 9), (6, 12), (12, 12), (12,6)\}$ is a relation on set $A = \{3, 6, 9, 12\}$ , then relation $R$ is