Could someone verify that my proof is valid as the question did not have a solution?
- $(\lnot R \lor \lnot F) \to (S \land L)$
- $(S \to T)$
- $(\lnot T)$
- $(\lnot S)$ 2,3 Modus tollens
- $\lnot (\lnot R \lor \lnot F) \lor (S \land L)$ 1, implication equivalence
- $(R \land F) \lor (S \land L)$ 5, double negation
- $(R \lor S)$ 6, simplification
- $(R)$ 7,4 Disjunctive syllogism
My main concern is with line 7 with the use of simplification, have I applied the rule correctly?
I understand that with simplification if you have $(P \land Q)$ and apply it, it returns $(P)$.
For my proof, you had to show that lines 1-3 (the hypotheses) entail $R$.