Relations

Let $A=\left\{\mathrm{1,} 2, \mathrm{3,} 4, 6\right\}$. Let $R$ be the relation on $A$ defined by $\left\{\right(a, b):a, b\in A, b$ is exactly divisible by $a\}$. Find the number of elements in the set of range of $R$.

Let $A=\left\{1, 2, \mathrm{3,} 4, 6\right\}.$ Let $R$ be the relation on $A$ defined by $\left\{\right(a, b):a, b\in A, b$is exactly divisible by $a\}$. Find the number of elements in the domain of $R$.

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

Write the relation $R=\left\{\right(x,x^3):x\mathrm{i}\mathrm{s}\mathrm{a}\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{n}10\}$ in roster form.

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

The figure shows a relationship between the sets $P$ and $Q.$ Write this relation
 In set-builder form. What is it’s domain and range?

$A=\{\mathrm{1,} 2, \mathrm{3,} 5\}$ and $B=\left\{\mathrm{4,} 6, 9\right\}.$ Define a relation $R$ from $A$ to $B$ by $R=\left\{\right(x, y):$ the difference between $x$ and $y$ is odd; $x\in A$, $y\in B$}. Write $R$ in roster form.

Define a relation $R$ on the set $N$ of natural numbers by
$R=\{\left(x, y\right) : y=x+5, x$ is a natural number less than $4$; $x, y\in N\}$. Depict this relationship using roster form. Write down the domain and the range.

Let $A=\{\mathrm{1,} 2, 3,....,14\}$. Define a relation $R$ from $A$ to $A$ by $R=\left\{\right(x, y) : 3x-y=0,\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}x, y\in A\}$. Write down its domain, codomain and range.