Let $A = \{1, 2, 3, 4, 5\}$. $A$ relation $R$ on $A$ is defined by $R = \{(x, y) | x, y \in A \text{ and } x < y\}$. Then $R$ is:

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 $N$ be the set of natural numbers and the relation $R$ on $N \times N$ is defined by $(a, b) R (c, d)$ if $ad(b + c) = bc(a + d)$. Then $R$ is:

If $R$ is an equivalence relation on a set $A$,then $R^{-1}$ is

Let $R$ be a relation from $A = \{2, 3, 4, 5\}$ to $B = \{3, 6, 7, 10\}$ defined by $R = \{(a, b) \mid a \text{ divides } b, a \in A, b \in B\}$. Then,the number of elements in $R^{-1}$ will be:

Let $R_{1} = \{(a, b) \in N \times N : |a - b| \leq 13\}$ and $R_{2} = \{(a, b) \in N \times N : |a - b| \neq 13\}$. Then on $N$: