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

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

Let $R$ be the relation on $Z$ defined by $R = \{ (a,b):a,b \in Z,a - b$ is an integer $\} $  Find the domain and range 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 $A=\{1,2,3,4\}, B=\{1,5,9,11,15,16\}$ and $f=\{(1,5),(2,9),(3,1),(4,5),(2,11)\}$
Are the following true?

$f$ is a relation from $A$ to $B$

Justify your answer in each case.

Write the relation $R = \{ \left( {x,{x^3}} \right):x$ is a prime number less than $10{\rm{\} }}$ in roster form.