Write the given set using rule method.

$\mathrm{X}=\left\{a, e, t\right\}$

Decide which of the following are equal sets and which are not? Justify your answer.

$\mathrm{A}=\left\{x | 3x-1=2\right\}$

$\mathrm{B}=\{x | x$ is a natural number but $x$ is neither prime nor composite$\}$

$\mathrm{C}=\left\{x | x\in \mathrm{N}, x<2\right\}$

Decide whether set $\mathrm{A}$ and $\mathrm{B}$ are equal sets. Give reason for your answer.

$\mathrm{A}=$ Even prime numbers

$\mathrm{B}=\left\{x | 7x-1=13\right\}$

Is the given set is an empty set? Give reason.

$\mathrm{A}=\left\{a\right|a$ is a natural number smaller than zero$\}$

Is the given set is an empty set? Give reason.

$\mathrm{B}=\left\{x | x^2=0\right\}$

Is the given set is an empty set? Give reason.

$\mathrm{C}=\left\{x | 5x-2=0, x\in \mathrm{N}\right\}$

Write with reasons, whether the given sets is finite or infinite.

$\mathrm{A}=\{x | x<10, x$ is a natural number$\}$

Write with reasons, the given set is finite or infinite.

$\mathrm{B}=\{y | y<-1,y$ is an integer$\}$

Write with reasons, the given set is finite or infinite.

$\mathrm{C}=$ Set of students of class $9$ from your school.