A combinational circuit is specified by the three Boolean functions:

F$($A$,$ B$,$ C$)=$ B$($A$+$ C$)+$ AB$+$ BC$$

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

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

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

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

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