Consider the following sentence:
$$[ ({Food} {\:\;{\Rightarrow}\:\;}{Party}) \lor ({Drinks} {\:\;{\Rightarrow}\:\;}{Party}) ] {\:\;{\Rightarrow}\:\;}[ ( {Food} \land {Drinks} ) {\:\;{\Rightarrow}\:\;}{Party}]\ .$$
1. Determine, using enumeration, whether this sentence is valid, satisfiable (but not valid), or unsatisfiable.
2. Convert the left-hand and right-hand sides of the main implication into CNF, showing each step, and explain how the results confirm your answer to (a).
3. Prove your answer to (a) using resolution.
$$[ ({Food} {\:\;{\Rightarrow}\:\;}{Party}) \lor ({Drinks} {\:\;{\Rightarrow}\:\;}{Party}) ] {\:\;{\Rightarrow}\:\;}[ ( {Food} \land {Drinks} ) {\:\;{\Rightarrow}\:\;}{Party}]\ .$$
1. Determine, using enumeration, whether this sentence is valid, satisfiable (but not valid), or unsatisfiable.
2. Convert the left-hand and right-hand sides of the main implication into CNF, showing each step, and explain how the results confirm your answer to (a).
3. Prove your answer to (a) using resolution.
Consider the following sentence:
$$[ ({Food} {\:\;{\Rightarrow}\:\;}{Party}) \lor ({Drinks} {\:\;{\Rightarrow}\:\;}{Party}) ] {\:\;{\Rightarrow}\:\;}[ ( {Food} \land {Drinks} ) {\:\;{\Rightarrow}\:\;}{Party}]\ .$$
1. Determine, using enumeration, whether this sentence is valid,
satisfiable (but not valid), or unsatisfiable.
2. Convert the left-hand and right-hand sides of the main implication
into CNF, showing each step, and explain how the results confirm
your answer to (a).
3. Prove your answer to (a) using resolution.