What is the minimum number of gates required to implement the boolean function $(AB + C)$, if we have to use only $2$- input NOR gates?

Consider the following Boolean function of four variables:

$f(w, x, y,z) = L\left(1,3,4,6,9,11,12,14\right)$

The function is:

Let $f(w, x, y, z) = r\left(0, 4, 5, 7, 8, 9, 13, 15\right)$. Which of the following expressions is/are not equivalent to $f$?

(P) $x\text{'}y\text{'}z\text{'} + w\text{'}xy\text{'} + wy\text{'}z+ xz$

(Q)$w\text{'}y\text{'}z\text{'}+wx\text{'}y\text{'}+xz$

(R) $w\text{'}y\text{'}z\text{'} + wx\text{'}y\text{'} + xyz + xy\text{'}z$

(S)$x\text{'}y\text{'}z\text{'} + wx\text{'}y\text{'} + w\text{'}y$

Define the connective $*$ for the Boolean variables X and Y as $X*Y = XY + X\text{'}Y\text{'}$. Let $Z = X*Y$ . Consider the following expressions P, Q and R

P:$X=Y*Z$ 

Q: $Y=X*Z$

R: $X*Y*Z=1$

Which of the following is true?