1. P $ \lor $ O
2. Q ⊃ ∼O
-Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?
A) O
B) P
C) Q
D) O ⊃ P
E) ∼Q $ \lor $ P

Question

Quizplus · Accepted Answer

Given the premises P $ \lor $ O and Q ⊃ ∼O, we can derive ∼Q $ \lor $ P using Disjunctive Syllogism (DS) and the rule of implication. If Q implies not O (Q ⊃ ∼O), and we have P or O (P $ \lor $ O), it logically follows that if not Q, then P must be true, hence ∼Q $ \lor $ P.

1 P ∨ \lor ∨ O 2 Q ⊃ ∼O -Which of the Following Propositions Is

1 P $\lor$ O
2 Q ⊃ ∼O
-Which of the Following Propositions Is