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:

Let $A = \{1, 2, 3, \ldots, 100\}$. Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $2x = 3y$. Let $R_1$ be a symmetric relation on $A$ such that $R \subset R_1$ and the number of elements in $R_1$ is $n$. Then,the minimum value of $n$ is:

Let $R_1$ and $R_2$ be two relations on a set $A$. Choose the incorrect statement.

Give an example of a relation that is symmetric and transitive but not reflexive.

Let $R = \{(1, 3), (2, 2), (3, 2)\}$ and $S = \{(2, 1), (3, 2), (2, 3)\}$ be two relations on the set $A = \{1, 2, 3\}$. Find $R \circ S^{-1}$.

Let $n$ be a fixed positive integer. The relation $R$ on the set of integers $Z$ is defined by $aRb \Leftrightarrow n | (a - b)$. Then $R$ is: