This is a simple propositional logic demonstration. I’d appreciate your help. I don’t know if my answer is correct, but the textbook used another demonstration.
- $T \vee R$
- $(T \vee R) \vee (S.P) \to (Q.S)$, therefore $Q.S$
- $T$ 1, Simplification
- $T \vee (S.P) \to (Q.S)$ 2, Simplification
- $T \to Q.S$ 2,4, Simplification
- $T$ 5, Modus Ponens
I know this is a very basic question and my answer is not elegant, but since I’m studying logic all by myself, and have no teacher to ask, I’d appreciate an answer.
The book made a more elegant and simple answer:
- $(T \vee R) \vee (S.P)$ 1, Addition
- $Q.S$ 2,3 Modus Ponens