Find the cardinal number of the set: The set of all vowels in the word $\mathrm{PRINCIPAL}$.

State whether the given statement is true or false. Justify your answer.

$37\notin \left\{x:x \mathrm{has} \mathrm{exactly} \mathrm{two} \mathrm{positive} \mathrm{factors}\right\}$

State whether the given statement is true or false. Justify your answer.

$35\in \left\{x:x \mathrm{has} \mathrm{exactly} \mathrm{four} \mathrm{positive} \mathrm{factors}\right\}$

State whether the given statement is true or false. Justify your answer.

$496\in \left\{y: \mathrm{the} \mathrm{sum} \mathrm{of} \mathrm{all} \mathrm{positive} \mathrm{factors} \mathrm{of} y \mathrm{is} 2y\right\}$

State whether the given statement is true or false. Justify your answer.

$3\notin \left\{x:x^4-5x^3+2x^2-112x+6=0\right\}$

Identify whether the given set is finite set or infinite set. In case of finite set, mention the cardinal number.

$A=\left\{x:x\in I,x<5\right\}$.