Let $R$ be an equivalence relation on a finite set $A$ having $n$ elements. Then the number of ordered pairs in $R$ 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

Let $R$ be an equivalence relation on a finite set $A$ having $n$ elements. Then the number of ordered pairs in $R$ is

Let $A = \{-4, -3, -2, 0, 1, 3, 4\}$ and $R = \{(a, b) \in A \times A : b = |a| \text{ or } b^2 = a + 1\}$ be a relation on $A$. Then the minimum number of elements that must be added to the relation $R$ so that it becomes reflexive and symmetric is $........$.

Let $A = \{1, 2, 3, 4\}$ and $R = \{(1, 2), (2, 3), (1, 4)\}$ be a relation on $A$. Let $S$ be the smallest equivalence relation on $A$ such that $R \subset S$. If the number of elements in $S$ is $n$,then the value of $n$ is:

If $R$ is an equivalence relation on a set $A$,then $R^{-1}$ is