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

For real numbers $x$ and $y$,we define the relation $R$ as $xRy$ if $x - y + \sqrt{2}$ is an irrational number. Then the relation $R$ 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:

Let $A = \{a, b, c\}$. The number of equivalence relations on $A$ containing $(b, c)$ is:

Let $A = \{1, 2, 3\}$. The number of relations on $A$ containing $(1, 2)$ which are symmetric and transitive but not reflexive is . . . . . . .

Give an example of a relation which is transitive but neither reflexive nor symmetric.