a$.(5$ points$)$ Use the sum of products to determine the simplified Boolean expression which will result in the truth table below.

b$.(5$ points$)$ Create a circuit using AND, OR$,$ NOT, X$-$OR$,$ or X$-$NOR gates to implement the resulting expression.

$\backslash$table$[[$A$,$B$,$C$,$Output$],[0,0,0,0],[0,0,1,1],[0,1,0,1],[0,1,1,0],[1,0,0,0],[1,0,1,1],[1,1,0,1],[1,1,1,0]]$