Types of Set

You are given two sets such that a set is not a subset of the other. If you have to prove this, how do you prove? Justify your answer.

Is any set subset to itself?

Is empty set subset to every set?

$A$ is the set of prime numbers less than $10$, $B$ is the set of odd numbers $<10$ and $C$ is the set of even numbers $<10$. How many of the following statements are true?

$$\begin{gathered} \left(i\right) A\subset B \\ \left(ii\right) B\subset A \\ \left(iii\right) A\subset C \\ \left(iv\right) C\subset A \\ \left(v\right) B\subset C \\ \left(vi\right) C\subset B \end{gathered}$$

$P$ is the set of factors of $5, Q$ is the set of factors of $25$ and $R$ is the set of factors of $125$. Which one of the following is false?

If $A=\left\{a, b, c, d\right\}$, then how many subsets does $A$ have?

$A=$ {set of quadrilaterals}, $B=$ {square, rectangle, trapezium, rhombus}. State whether $A\subset B$ or $B\subset A$. Justify your answer.

State whether the statement is true or false.

$0=\left\{0\right\}$

State whether the statement is true or false.

$\varphi =0$

State whether the statement is true or false.

$\left\{\right\}=\varphi$

If $A$ and $B$ are disjoint sets, then how can you find $(A\cup B)$.

What is the relation between $\mathrm{n}\left(\mathrm{A}\right), \mathrm{n}\left(\mathrm{B}\right), \mathrm{n}(\mathrm{A}\cap \mathrm{B})$ and $\mathrm{n}(\mathrm{A}\cup \mathrm{B})$.

State whether the following set is a finite or an infinite set.

The set of circles passing through the origin $\left(0,0\right)$.

State whether the following set is a finite or an infinite set.

The set of numbers which are multiples of $5$

State whether the following set is a finite or an infinite set.

The set of lines which are parallel to the $X$-axis.

State whether the following set is a finite or an infinite set.

The set of letters in the English alphabet.

State whether the following set is a finite or an infinite set.

The set of prime numbers smaller than $99$

State whether the following set is a finite or an infinite set.

$\{1, 2, 3, \dots , 99, 100\}$

State whether the following set is empty or not.

State whether the following set is a finite or an infinite set.

The set of months in a year.