$(5$ points$)$ Is $(p^{{?}^{?}}q)(pvvr)$ a tautology? Prove or disprove it$.$

$3(10$ points$)$ Suppose xinZ,yinZ,zinZ, function $P(x,y)$ is $x+y^2+z=1.$ Determine the truth value of the follows and explain why.

AAxEEyEEzP$(x,y,z)$

AAxAAyEEzP$(x,y,z)$

AAxAAzEEyP$(x,y,z)$

EExEEyAAzP$(x,y)$