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\,\} $
Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then
Write the following sets in the set-builder form :
$\{ 1,4,9 \ldots 100\} $
Write the solution set of the equation ${x^2} + x - 2 = 0$ in roster form.
The smallest set $A$ such that $A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}$ is