A combinational circuit is specified by the three Boolean functions:

$F(A,B,C)=A^{\text{'}}(B+C)+AB$

$G(A,B,C)=$ABC$+BC$

$H(A,B,C)=Ao+B$

a$.(15$ points$)$ Create a truth table for the circuit.

b$.(15$ points$)$ Simplify the expressions using Karnaugh maps.

c$.(15$ points$)$ Draw the logic diagram for the circuit using the simplified expressions obtained in part b$.$