[(P ⊃ Q) ⊃ Q] ⊃ (P $ \lor $ Q)
-Which of the following propositions is an appropriate assumption for a conditional proof of the given logical truth?
A) P
B) P ⊃ Q
C) (P ⊃ Q) ⊃ Q
D) [(P ⊃ Q) ⊃ Q] ⊃ P
E) [(P ⊃ Q) ⊃ Q] ⊃ (P $ \lor $ Q)

Question

Quizplus · Accepted Answer

The assumption for a conditional proof needs to be a statement that when assumed true, allows for the conclusion to be deduced. In this case, assuming (P ⊃ Q) ⊃ Q to be true allows us to use modus ponens to deduce both P and Q, which in turn allows us to use disjunctive syllogism to deduce P $ \lor $ Q. The other options do not provide a direct path to the conclusion.

[(P ⊃ Q) ⊃ Q] ⊃ (P ∨ \lor ∨ Q) -Which of the Following Propositions Is an Appropriate Assumption

[(P ⊃ Q) ⊃ Q] ⊃ (P $\lor$ Q)
-Which of the Following Propositions Is an Appropriate Assumption