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 $(b, a) \in R$

The relation $R$ defined on the set of natural numbers as $\{(a, b) : a$ differs from $b$ by $3\}$, is given by

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

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 $R$

The Fig shows a relationship between the sets $P$ and $Q .$ Write this relation

in set-builder form 

What is its domain and range?

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