1. A ⊃ (B $ \lor $ C)
2. ∼A $ \lor $ (D $ \lor $ E)
3. ∼(C $ \lor $ E)
-Consider assuming 'A' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
A) B $ \lor $ C
B) ∼∼A
C) ∼C • ∼E
D) All of the above
E) Options A and B, but not option C

Question

Quizplus · Accepted Answer

With the assumption of 'A' for conditional proof, all the given options become immediate consequences. Option A is directly derived from the first premise by modus ponendo ponens, given the assumption of 'A'. Option B is a direct consequence of assuming 'A', as double negation simply removes the negation. Option C is derived from the third premise using De Morgan's laws.

1 a ⊃ (B ∨ \lor ∨ C) 2 ∼A ∨ \lor ∨

1 a ⊃ (B $\lor$ C)
2 ∼A $\lor$