Subsets

The improper subset of the set $C=\left\{m, 1, 4\right\}$ is

If a set admits only one proper subset, then the set must be

If $X=\left\{a, b, c\right\}$, then the number of proper subets of $X$ is

The number of possible subsets of the set $\varphi$ is

If $A=\left\{p, q, \left\{p, q\right\}\right\}$, then the number of subsets of $A$ is

If $n(A\cup B)=n\left(A\right)-n\left(B\right)$ then find $B$.

Let $A$ and $B$ be subsets of the universal set $X,$ where $\mathrm{X}=\{x\mid x$ is an integer and $-5<x<6\}$

$A=\left\{x\mid \frac{x}{2}\mathrm{is} \mathrm{an} \mathrm{integer}\right\}$ and $B=\left\{x\mid \frac{x}{2}\mathrm{is} \mathrm{a} \mathrm{positive} \mathrm{integer}\right\}$ find all the subsets of $B$.

Cheek the truth of the following statements with proper justification:

Any subset of an infinite set must be infinite.

Cheek the truth of the following statements with proper justification:

There may be an infinite subset of a finite set.

If $A\subseteq B$ then $A\cup B=$

Does there exist any set $A$ such that it has exactly $5$ subsets? Justify your answer.

Write all possible proper subsets of $\{x, y, z\}$.

Write all possible subsets of the following sets:

$\left\{0\right\}$

Write all possible subsets of the following sets:

$\{2, 5\}$

Let $P$  be the set of all prime integers. Does there exist some $x\in P$ such that,

$\{x, x+2\}\subseteq P$?

Let $P$  be the set of all prime integers. Does there exist some $x\in P$ such that,

$\{x, x+1, x+2\}\subseteq P$?

Let $P$  be the set of all prime integers. Does there exist some $x\in P$ such that,

$\{x, x+1\}\subseteq P$?

If $A$ is a finite set such that $\left|A\right|=5,$ find $\left|\mathcal{P}\right(A\left)\right|$

Does every non-empty set admit a proper subset? Give an example of a set that has only one subset.

Cotyledons are also called-