QUESTION $14$

Given the following parse tree, which option below gives the associated propositional logic sentence?

Option $1$: not$(not(q^{{?}^{?}}(pr){)}^{{?}^{?}}(rq))$

Option $2$: not$(not{q}^{{?}^{?}}(pr){)}^{{?}^{?}}(rq)$

Option $3$: not$((not(q^{{?}^{?}}(pr){)}^{{?}^{?}}(rq)))$

Option $4$: not$((not{q}^{{?}^{?}}(pr){)}^{{?}^{?}}(rq))$

QUESTION $15$

Consider the following sequent and then choose the correct option below.

$(p^{{?}^{?}}q)s,$nots$|--$pvvnotq

Option $1$: The sequent is valid and can be formally proved using natural deduction rules.

Option $2$: The sequent is valid because the relation $(p^{{?}^{?}}q)s,$nots$|==$pvvnotq

holds as shown by the following valuation: $p=F,q=F,s=F.$

Option $3$: The sequent is not valid because the relation $(p^{{?}^{?}}q)s,$nots$$pvvnotq

does not hold as shown by the following valuation: $p=F,q=T,s=F.$

Option $4$: The sequent is not valid because the relation $(p^{{?}^{?}}q)s,$nots$$pvvnotq

does not hold as shown by the following valuation: $p=F,q=T,s=T.$