Examine whether the following statements are true or false :

$\{ 1,2,3\}  \subset \{ 1,3,5\} $

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\,\} $

How many elements has $P(A),$ if $A=\varnothing ?$

Which of the following pairs of sets are equal ? Justify your answer.

$A = \{ \,n:n \in Z$ and ${n^2}\, \le \,4\,\} $ and $B = \{ \,x:x \in R$ and ${x^2} - 3x + 2 = 0\,\} .$

Are the following pair of sets equal ? Give reasons.

$A = \{ x:x$ is a letter in the word ${\rm{FOLLOW }}\} $

$B = \{ y:y$ is a letter in the word $WOLF\} $

Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?

$\{ 3,4\}  \subset A$