For real numbers $x$ and $y$, we write $ xRy \in $ $x - y + \sqrt 2 $ is an irrational number. Then the relation $R$ is
Reflexive
Symmetric
Transitive
None of these
Let $R =\{( P , Q ) \mid P$ and $Q$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of $(1,-1)$ is the set
Let $R$ be a reflexive relation on a set $A$ and $I$ be the identity relation on $A$. Then
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
Maximum number of equivalence relations on set $A = \{1, 2, 3, 4\}$ is $N$, then -
Let $A = \{ 2,\,4,\,6,\,8\} $. $A$ relation $R$ on $A$ is defined by $R = \{ (2,\,4),\,(4,\,2),\,(4,\,6),\,(6,\,4)\} $. Then $R$ is