Question $3[10$ points$]$

Consider the propositional logic formula:

$(PvvQ{)}^{{?}^{?}}(notPvvQvvR{)}^{{?}^{?}}(notQvvR{)}^{{?}^{?}}(notR{)}^{{?}^{?}}(SvvT{)}^{{?}^{?}}(notSvvnotT)$

For this formula, use the Davis$-$Putnam$-$Logemann$-$Loveland $($DPLL$)$ algorithm to check

for its satisfiability. Justify each step of your answer. If satisfiable, provide an assignment

to P$,$ Q$,$ and R that makes the formula "True." If not, show where the DPLL algorithm

aborts.

Question $4[10$ points$]$

Mark the following statements as either True or False.

a$)(Pvv{Q}^{{?}^{?}}R{)}^{{?}^{?}}(notPvvS{)}^{{?}^{?}}(EvvFvv{G}^{{?}^{?}}H{)}^{{?}^{?}}(IvvJ{)}^{{?}^{?}}(notKvvnotL)$ is in

conjunctive normal form $($CNF$).$

b$)$ The Law of Excluded Middle states that every proposition must be either true or false.

c$)A(B^{{?}^{?}}C)$ is semantically equivalent to notC$(not{B}^{{?}^{?}}$notA$).$

d$)$ Consider the following logical argument:

All online systems require internet connectivity to function properly.

The library catalog system is an online system.

Therefore, the library catalog system requires internet connectivity to function properly.

Note: The above logical argument is an example of the application of the modus tollens

rule.

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