Let $R$ and $S$ be two relations on a set $A$. Then
$R$ and $S$ are transitive, then $R \cap S $ is also transitive
$R$ and $S$ are reflexive, then $R \cap S $ is also reflexive
$R$ and $S$ are symmetric then $R \cup S $ is also symmetric
All of these
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
Show that the number of equivalence relation in the set $\{1,2,3\} $ containing $(1,2)$ and $(2,1)$ is two.
Let $R$ be a relation defined on $N \times N$ by $(a, b) R(c, d) \Leftrightarrow a(b + c) = c(a + d).$ Then $R$ is
$A$ relation $R$ is defined from $\{2, 3, 4, 5\}$ to $\{3, 6, 7, 10\}$ by $xRy \Leftrightarrow x$ is relatively prime to $y$. Then domain of $R$ is
Let $R = \{ (3,\,3),\;(6,\;6),\;(9,\,9),\;(12,\,12),\;(6,\,12),\;(3,\,9),(3,\,12),\,(3,\,6)\} $ be a relation on the set $A = \{ 3,\,6,\,9,\,12\} $. The relation is