On the set $N$ of natural numbers,the relation $R$ is defined by $nRm$ if $n$ is a factor of $m$ (i.e.,$n|m$). Then $R$ is:

The relation $S$ in the set $R$ of real numbers,defined as $S = \{(a, b) : a < b^2\}$ is a . . . . . . relation.

Let $A = \{2, 3, 4, 5, \ldots, 30\}$ and $\simeq$ be an equivalence relation on $A \times A$,defined by $(a, b) \simeq (c, d)$ if and only if $ad = bc$. Then the number of ordered pairs $(c, d)$ which satisfy this equivalence relation with the ordered pair $(4, 3)$ is equal to:

Show that the relation $R$ in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)\}$ is reflexive but neither symmetric nor transitive.

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

On the set $R$ of real numbers,the relation $\rho$ is defined by $x \rho y$ if $x > |y|$. Which of the following statements is true regarding the properties of $\rho$?