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 set $A = A_{1} \cup A_{2} \cup \ldots \cup A_{k}$,where $A_{i} \cap A_{j} = \phi$ for $i \neq j$ and $1 \leq i, j \leq k$. Define the relation $R$ from $A$ to $A$ by $R = \{(x, y) : y \in A_{i} \text{ if and only if } x \in A_{i}, 1 \leq i \leq k\}$. Then,$R$ is

If $n(A) = m$,then the total number of reflexive relations that can be defined on $A$ is-

If a relation $R$ on the set $\{1, 2, 3\}$ is defined by $R = \{(1, 1)\}$,then $R$ is

The number of relations,defined on the set ${a, b, c, d}$,which are both reflexive and symmetric,is equal to:

The number of symmetric relations defined on the set $\{1, 2, 3, 4\}$ which are not reflexive is