Let $R=\left\{\right(a, b): a, b\in Z$ and $b=2a-4\}$. If  $(a, -2)\in R$ and $\left(4, b^2\right)\in R$. Then, write the values of $a$ and $b$.

Let $R$ be a relation on $Z$, defined by $(x, y)\in R\iff x^2+y^2=9$. Then, write $R$ as set of ordered pairs.

Let $A$ be the set of first five natural numbers and let $R$ be a relation on $A$, defined by $(x, y)\in R\iff x\le y$.

Express $R$ and $R^{-1}$ as sets of ordered pairs.

Find domain $\left(R^{-1}\right)$ and range $\left(R\right)$.

Let $R=\left\{\right(x, y): x, y\in Z$ and $\left.x^2+y^2=25\right\}$.

Express $R$ and $R^{-1}$ as sets of ordered pairs. Show that $R=R^{-1}$.

Find $R^{-1}$, when $R=\left\{\right(1, 2), (1, 3), (2, 3), (3, 2), (4, 5\left)\right\}$,

Find $R^{-1}$, when $R=\left\{\right(x, y): x, y\in N, x+2y=8\}$.

Let $A=\{a, b\}$. List all relations on $A$.

Let $R=\left\{\right(a, b): a, b\in N$ and $a<b\}$.

Show that $R$ is a binary relation on $N$, which is neither reflexive nor symmetric.

Let $A$ and $B$ be two sets such that $n\left(A\right)=5, n\left(B\right)=3$ and $n(A\cap B)=2$. find $n(A\cup B)$.