Let $R_1$ and $R_2$ be two relations on a set $A$ , then choose incorrect statement
If $R_1$ and $R_2$ are transitive, then ${R_1} \cap {R_2}$ is also transitive
If $R_1$ and $R_2$ are reflexive, then ${R_1} \cup {R_2}$ is also reflexive.
If $R_1$ and $R_2$ are symmetric, then ${R_1} \cap {R_2}$ is also symmetric
If $R_1$ and $R_2$ are equivalence, then ${R_1} \cup {R_2}$ is also equivalence
Let $R$ be a relation from $A = \{2,3,4,5\}$ to $B = \{3,6,7,10\}$ defined by $R = \{(a,b) |$ $a$ divides $b, a \in A, b \in B\}$, then number of elements in $R^{-1}$ will be-
The relation "congruence modulo $m$" is
Show that the relation $R$ in the set $\{1,2,3\}$ given by $R =\{(1,1),\,(2,2),$ $(3,3)$, $(1,2)$, $(2,3)\}$ is reflexive but neither symmetric nor transitive.
The relation "less than" in the set of natural numbers is
Let $R$ be a relation on the set $N$ of natural numbers defined by $nRm $$\Leftrightarrow$ $n$ is a factor of $m$ (i.e.,$ n|m$). Then $R$ is