Define Power set of a set. Write down the power set of $A=\left\{a, b, c\right\}$. 

Show the relationship among the following three sets in respect of subsets and supersets:

$\mathrm{N}=\left\{\mathrm{x}: \mathrm{x} \mathrm{is} \mathrm{a} \mathrm{natural} \mathrm{number}\right\}$

$\mathrm{Z}=\left\{\mathrm{x}: \mathrm{x} \mathrm{is} \mathrm{an} \mathrm{integer}\right\}$

$\mathrm{Q}=\left\{\mathrm{x}: \mathrm{x} \mathrm{is} \mathrm{a} \mathrm{rational} \mathrm{number}\right\}$

$\mathrm{R}=\left\{\mathrm{x}: \mathrm{x} \mathrm{is} \mathrm{a} \mathrm{real} \mathrm{number}\right\}$

Find which of the following sets are equal and which are unequal:

$A=\left\{3, 2, 5\right\}$

$B=\left\{3, 5, 0\right\}$

$C=\left\{\mathrm{x}: \mathrm{x}\left({\mathrm{x}}^2-8\mathrm{x}+15\right)=0\right\}$

$D=\left\{2, 5, 3\right\}$

Write down all the subsets of the following set:

$\left\{2\right\}$

Write down also the proper subsets.

Write down all the subsets of the following set:

$\left\{3, 4\right\}$

Write down also the proper subsets.

Write down all the subsets of the following set:

$\left\{2, 3, 4\right\}$

Write down also the proper subsets.

Give an example to show that $A\subset B, B\subset C\Rightarrow A\subset C$.

If $a\in A$ and $a\in B$, does it follow that $A\subseteq B$? Give reasons.