Final answer:
To determine the logical sentence's validity, we use enumeration to test all truth possibilities, convert it to CNF checking for satisfiability, and employ resolution to test for unsatisfiability.
Step-by-step explanation:
When analyzing the logical sentence: [( Food ⇒ Party) ∧ (Drinks ⇒ Party) ∨ (Music ⇒ Party)] ⇒ [( Food ∧ Music ∧ Drinks) ⇒ Party], we need to determine if this compound sentence is valid, satisfiable, or unsatisfiable by assessing whether the truth of the premises necessitates the truth of the conclusion. Using enumeration, we explore all possible truth values for the atomic sentences involved and observe the resulting truth of the entire sentence.
To convert into CNF (Conjunctive Normal Form), we would apply logical equivalences such as De Morgan's law, distribution, and double negation to the sentence, obtaining a conjunction of clauses. For example, the left-hand side (Food ⇒ Party) can be converted into CNF by first rewriting it as ¬Food ∨ Party (using implication elimination) and proceeding with any required transformations.
To prove using resolution, we would convert all sub-sentences into clauses and apply the resolution rule which states that if we have a clause containing a literal and another clause containing the negation of that literal, they can be resolved to produce a new clause containing the remaining literals from both clauses. This process is iterated until either we derive a contradiction (proving that the original sentence is unsatisfiable), or we can no longer derive new clauses (in which case the sentence is satisfiable).