1. (∀x)[(Px $ \lor $ Qx) ⊃ (Rx • ∼Sx)]
2. (∀x)[Rx ⊃ (Tx ⊃ ∼Sx)]
-Consider assuming 'Px' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in M of the given premises with that further assumption for conditional proof?
A) Ra ⊃ (Tb ⊃ ∼Sc)
B) (∀x)Px
C) Px $ \lor $ Qx
D) Tx ⊃ ∼Sx
E) Rx • ∼Sx

Question

Quizplus · Accepted Answer

Given the assumption 'Px' for conditional proof, the immediate one-step consequence in M of the given premises is 'Px $ \lor $ Qx'. This follows directly from the rules of disjunction introduction, where assuming 'Px' allows us to infer 'Px $ \lor $ Qx' without needing to reference the other premises.

1 (∀X)[(Px ∨ \lor ∨ Qx) ⊃ (Rx • ∼Sx)] 2 ∨ \lor ∨

1 (∀X)[(Px $\lor$ Qx) ⊃ (Rx • ∼Sx)]
2 $\lor$