The number of elements in the set $\{x \in R :(|x|-3)|x+4|=6\}$ is equal to

Examine whether the following statements are true or false :

$\{ a,e\}  \subset \{ x:x$ is a vowelin the English alphabet $\} $

Let $S = \{ 0,\,1,\,5,\,4,\,7\} $. Then the total number of subsets of $S$ is

Examine whether the following statements are true or false :

$\{a\} \subset\{a, b, c\}$

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

$1 \subset A$

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 $A \not\subset B$ and $B \not\subset C,$ then $A \not\subset C$