Let $A=(1, 3, 4)$ and $B (2, 5, 7)$. Find the number of relations from $A$ to $B$.

Find the identity relation on the set $A=\left\{5,6,7\right\}$

Let $A=\left\{2,3,4\right\}$ and $B=\left\{1,2,5,6\right\}$ and let $R=\left\{\left(a,b\right):a\in A,b\in B,a<b\right\}$ be relation from $A$ to $B.$ Find $R,$ the domain of $R$ and its range. What will be the relation of $a>b$ instead of $a<b.$

Let $A=\left\{1,2,3,5\right\}$ and $B=\left\{2,4,6,10\right\}$. Let $R=\left\{\left(a,b\right):a\in A,b\in B,a \text{divides} b\right\}$ be relation from $A$ to $B.$ Find $R,$ and show that domain of $R$ is $A$ and range of $R$ is $B.$

Let $R$ be the relation on the set $N$ of natural numbers defined by $a+3b=12.$ Find $R.$

Let $R$ be the relation on the set $N$ of natural numbers defined by $a+3b=12.$ Find the range of $R.$

Let $R$ be the relation on the set $N$ of natural numbers defined by $a+3b=12.$ Find the domain of $R.$

A relation $R$ is defined from a set $A=\left\{2,6,8,10\right\}$ to a set $B=\left\{2,3,4,5\right\}$ by $R=\left\{\left(a,b\right):a\in A,b\in B,a \text{is divisible by} b\right\}$. Find $R$ as a set of ordered pairs. Find also the domain and range of $R$.