$1.(2$ points$)$ What is the Boolean expression for P$?$

x y z P

$0001$

$0010$

$0100$

$0111$

$1000$

$1010$

$1101$

$1110$

Design a circuit that can produce output P for inputs x$,$ y$,$ and z as expressed in the table above.

Hint:

$1.$ When X$=0,$ Y$=0,$ and Z$=0,$ P$=1.$

$2.$ When X$=0,$ Y$=1,$ and Z$=1,$ P$=1.$

$3.$ When X$=1,$ Y$=1,$ and Z$=0,$ P$=1.$