1. P $ \lor $ (Q ⊃ R)
2. R ⊃ (S • T)
3. ∼P
-Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS)?
A) Q
B) R
C) S
D) T
E) Q ⊃ (S • T)

Question

Quizplus · Accepted Answer

From premise 1, we can use DS (disjunctive syllogism) to get Q ⊃ R. From premise 2, we can use MP (modus ponens) with R ⊃ (S • T) to get S • T. In combination with Q ⊃ R from the previous step, we can use MP again to get Q ⊃ (S • T). Finally, from premise 3, we have ∼P, which means we can use MT (modus tollens) with Q ⊃ R to get ∼Q. Therefore, we can combine ∼Q and Q ⊃ (S • T) to get Q ⊃ (S • T) as the derivable proposition.

1 P ∨ \lor ∨ (Q ⊃ R) 2

1 P $\lor$ (Q ⊃ R)
2