$A = \{ x:x \ne x\} $ represents

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If $x \in A$ and $A \not\subset B$, then $x \in B$

Write the set $A = \{ 1,4,9,16,25, \ldots .\} $ in set-builder form.

Given the sets $A=\{1,3,5\}, B=\{2,4,6\}$ and $C=\{0,2,4,6,8\},$ which of the following may be considered as universal set $(s)$ for all the three sets $A$, $B$ and $C$

$\{0,1,2,3,4,5,6,7,8,9,10\}$

Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:

$\{ x:x$ is a student of class $\mathrm{XI}$ of your school $\}  \ldots \{ x:x$ student of your school $\} $

In the following state whether $\mathrm{A = B}$ or not :

$A = \{ 2,4,6,8,10\} ;B = \{ x:x$ is positiveeven integer and $x\, \le \,10\} $