Question $4(10$ points$)$

Use propositional logic to prove the following arguments are valid

$($a$)(A^2{B}^{\text{'}}{)}^{{?}^{?}}B[(AC)C]$

$($b$)(Pvv(Q^{{?}^{?}}R){)}^{{?}^{?}}(R^{\text{'}}vvS{)}^{{?}^{?}}(S{T}^{\text{'}})(TP)$

Question $5(20$ points$)$

Write the argument using propositional wffs $($using the statement letters shown$).$ Then prove the

argument is valid using propositional logic.

$($a$)$ If chicken is on the menu, then don't order fish, but you should have either fish or salad. So if

chicken is on the menu have salad. $(C,F,S)$

$($b$)$ If a Democrat is elected then taxes will go up$.$ Either a Democrat will be elected or the bill will

pass. Therefore if taxes do not go up then the bill will pass. $(D,T,B)$

$($c$)$ It is not the case that if electric rates go up$,$ then usage will go down, nor is it true that either

new power plants will be built or bills will not be late. Therefore usage will not go down and bills

will be late. $(R,U,P,B)$

$($d$)$ If birds are flying south and the leaves are turning, then it must be fall. Fall brings cold weather.

The leaves are turning but the weather is not cold. Therefore, the birds are not flying south. $($B$,$

$L,F,C$