By using $1OR$ gate, $3$ XOR gates, and $3$AND gate, answer the following question: a$)$ By using the provided gate above, design a circuit diagram for the Boolean function: $F(A,B,C)=A*B+(Ao+C)$

b$)$ By using answer in Question $2$a$),$ create a truth table for the Boolean function F$($A$,$B$,$C$).$

c$)$ Write the simplified Boolean expression for F$($A$,$B$,$C$)$ using Boolean identity based on the truth table in Question $2($b$).$