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$).$

a b c g

$00001$

$10011$

$20100$

$30110$

$41001$

$51011$

$61101$

$71110$

d$)$ Show the minterms of the complement of each function in numeric form.

e$)$ Show the canonical algebraic expression in product of sums form.

f$)$ Show a minimum POS expression $($F: $2$ terms, $4$ literals; G: $2$terms, $4$ literals$)$