Which of the following are sets ? Justify your answer.

The collection of all natural numbers less than $100 .$

Which of the following are examples of the null set

$\{ y:y$ is a point common to any two parallellines $\} $

If $Q = \left\{ {x:x = {1 \over y},\,{\rm{where \,\,}}y \in N} \right\}$, then

Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:

$ 4\, ......... \, A $

Find the pairs of equal sets, if any, give reasons:

$A = \{ 0\} ,$

$B = \{ x:x\, > \,15$ and $x\, < \,5\} $

$C = \{ x:x - 5 = 0\} ,$

$D = \left\{ {x:{x^2} = 25} \right\}$

$E = \{ \,x:x$ is an integral positive root of the equation ${x^2} - 2x - 15 = 0\,\} $

Write the following intervals in set-builder form :

$\left( {6,12} \right]$