$[6]$ Given the following truth table:

a$.$ Write the Boolean expression for $x$ in terms of $A,B,$ and $C.$

b$.$ Simplify the expression as much as possible using the properties of Boolean algebra so it could be built with the minimum number of gates.

c$.$ Draw the logic diagram for the simplified expression.

$\backslash$table$[[$A$,$B$,$C$,x$