For a homework assignment I have to prove that one of the statements entails the other.
The statements are:
$(A \lor B) \to C$
$(A \to C) \lor (B \to C)$
The only thing that I got so far is either $\lnot(A \lor B) \to C$ or $(A \to C) \land (B \to C)$.
I can use the rules of Modus Ponens, Modus Tollens, Simplification, Conjunction, Disjunction, Conjunctive and Disjunctive Syllogism, Hypothethical Syllogism and Conditional Proof.
The equivalence rules I can use are Double Negation, De Morgan's Laws, Biconditional Equivalence,and I think, Transposition and Material Implication, too.
Is there someone who can help me? I've tried so much already...
The answer they wanted to hear was:
- (A v B) -> C
- A supp/CP
- A v B disj
- C 1,3MP
- A -> C 2-4 CP
- (A -> C) v (B -> C) 5 disj