Relation $R = \{(a, b): a < b\}$ is defined on the set of real numbers. Then $R$ is . . . . . . .

Give an example of a relation on a set $A = \{5, 6, 7\}$ which is symmetric but neither reflexive nor transitive.

Let $R = \{(a, a)\}$ be a relation on a set $A$. Then $R$ is:

Let the relations $R_1$ and $R_2$ on the set $X = \{1, 2, 3, \ldots, 20\}$ be given by $R_1 = \{(x, y) : 2x - 3y = 2\}$ and $R_2 = \{(x, y) : -5x + 4y = 0\}$. If $M$ and $N$ are the minimum number of elements required to be added to $R_1$ and $R_2$,respectively,to make the relations symmetric,then $M + N$ equals

Give an example of a relation on a set $A = \{4, 6, 8\}$ which is reflexive and symmetric but not transitive.

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