$1.(20$ points$)$ Implement the following functions with two $4-$to$-1-$line multiplexers and a single inverter:

F $=$ AB$\text{'}+$ C

G $=$ AC$\text{'}+$ B

a$.(10$ points$)$ Create the truth table for the two functions.

b$.(10$ points$)$ Implement the two functions with two $4-$to$-1$ line multiplexers and a single inverter.