Chapter $2,$ problem $15$: $(6+6$ pts$)$ For each of the following functions:

F $=$ AB$\text{'}+$ BC $+$ AC

G $=($A $+$ B$)($A $+$ C$\text{'})+$ AB$\text{'}$

a$)$ Show the truth table.

b$)$ Show the canonical algebraic expression in sum of products form.

c$)$ Show a minimum SOP expression $($F: $2$ terms, $4$ literals; G: $2$ terms, $3$ literals$).$