$3$a$)$ Design a circuit to implement the following boolean expression.

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

i$)$ using a $8$:$1$ multiplexer

ii$)$Using a $4$:$1$ multiplexer

iii$)$ Using a decoder

B$)$ Use a k$-$map to simplify the following boolean expressions and sketch the logic circuit for the simplified expression.

Y$($A$,$B$,$C$)=$ A'B'C $+$ A'BC' $+$ ABC