Subsets

Match the following sets for all sets $A, B$ and $C$

Given the sets $A=\{1, 3, 5\}, B=\{2, 4, 6\}$ and $C=\{0, 2, 4, 6, 8\}$. Then the universal set of all the three sets $A, B$ and $C$ can be _____.

Number of power set of the set $\mathrm{A}=\{1, 2\}$ is _____

When $A=\varphi$, then number of elements in $P\left(A\right)$ is _____.

Two finite sets have $m$ and $n$ elements. The number of subsets of the first set is $112$ more than that of the second set. The values of $m$ and $n$ are, respectively,

Determine whether the statement is true or false. Justify your answer

For all sets $A, B$ and $C$, if $A\subset C$ and $B\subset C$ then $A\cup B\subset C$

Determine whether each of the statements in these exercises is true or false. Justify your answer.

For all sets $A, B$ and $C$, if $A\subset B$ then, $A\cup C\subset B\cup C$

For all sets $A, B$ and $C$, $A\subset B,$ then $A\cap C\subset B\cap C$

Given that $\mathrm{N}=\{1, 2, 3, \dots ,100\}$. Then write

the subset of $\mathrm{N}$ whose element are perfect square numbers.

Given that $\mathrm{N}=\{1, 2, 3, \dots ,100\}$. Then write the subset of $\mathrm{N}$ whose elements are even numbers.

If $\mathrm{A}$ and $\mathrm{B}$ are subsets of the universal set $\cup$, then show that

$(\mathrm{A}\cap \mathrm{B})\subset \mathrm{A}$

If $\mathrm{A}$ and $\mathrm{B}$ are subsets of the universal set $\cup$, then show that

$\mathrm{A}\subset \mathrm{B}\iff \mathrm{A}\cup \mathrm{B}=\mathrm{B}$

If $\mathrm{A}$ and $\mathrm{B}$ are subsets of the universal set $\mathrm{U}$, then show that

$\mathrm{A}\subset \mathrm{A}\cup \mathrm{B}$