Maximum number of equivalence relations on set $A = \{1, 2, 3, 4\}$ is $N$, then -

Let $X$ be a family of sets and $R$ be a relation on $X$ defined by $‘A$ is disjoint from $B’$. Then $R$ is

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 number of relations, on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is

Let $A = \{a, b, c\}$ and $B = \{1, 2\}$. Consider a relation $R$ defined from set $A$ to set $B$. Then $R$ is equal to set

Let $R$ be a relation on the set of all natural numbers given by $\alpha b \Leftrightarrow \alpha$ divides $b^2$.

Which of the following properties does $R$ satisfy?

$I.$ Reflexivity   $II.$ Symmetry   $III.$ Transitivity