Consider this truth table:

$\backslash$table$[[$Inputs$,$Output$],[$x$,$Y$,$Z$,$F$],[0,0,0,1],[0,0,1,1],[0,1,0,0],[0,1,1,0],[1,0,0,1],[1,0,1,1],[1,1,0,0],[1,1,1,0]]$

a$.(5$ points$)$ Write the Boolean equation from the truth table using the sum of products method.

b$.(5$ points$)$ Simplify the equation using the Theorems and Axioms of Boolean algebra. State the theorems and axioms used.

c$.(5$ points$)$ Write the Boolean equation from the truth table using a Karnaugh map.

d$.(5$ points$)$ Do the equations from parts $b$ and $c$ agree? If not, then can you transform one of the equations into the other?