Let $R$ be a relation from $Q$ to $Q$ defined by $R=\{(a, b): a, b \in Q$ and $a-b \in Z \} .$ Show that

$(a, b) \in R$ implies that $(b, a) \in R$

Let $A=\{1,2,3,4,6\} .$ Let $R$ be the relation on $A$ defined by $\{ (a,b):a,b \in A,b$ is exactly divisible by $a\} $

Find the domain of $R$

Given two finite sets $A$ and $B$ such that $n(A) = 2, n(B) = 3$. Then total number of relations from $A$ to $B$ is

Let $A=\{1,2\}$ and $B=\{3,4\} .$ Find the number of relations from $A$ to $B .$

Let $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$

Depict this relation using an arrow diagram.

Let $A=\{1,2,3, \ldots, 14\} .$ Define a relation $R$ from $A$ to $A$ by $R = \{ (x,y):3x - y = 0,$ where $x,y \in A\} .$ Write down its domain, codomain and range.