State the truth value of the following statements. Working$/$explanation is not required.

$($a$)$ In the following set of question, assume the universe of discourse to be $N.$

i$.(\frac{1}{2}$ mark$)$ AAxEEy,$(x^2=y).$

True False

ii$.$ mark$)$ AAxEEyEEz,$\frac{x+y}{2}=z.$

True False

iii. $(\frac{1}{2}$ mark$)$ AAxAAzEEy,$x^2+y^2=z^2.$

True False

iv$.$ mark$)$