1. A ⊃ (B $ \lor $ ∼C)
2. D ⊃ (∼B • ∼E)
-Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
A) (A • D) ⊃ ∼(B $ \lor $ ∼E)
B) (A • D) ⊃ ∼(C $ \lor $ E)
C) (A • D) ⊃ ∼(B $ \lor $ ∼C)
D) (A • D) ⊃ ∼(D $ \lor $ B)
E) (A • D) ⊃ ∼(E $ \lor $ D)

Question

Quizplus · Accepted Answer

Given the premises A ⊃ (B $ \lor $ ∼C) and D ⊃ (∼B • ∼E), we can derive that if both A and D are true, then both conditions they imply must also be true. From A, we get B $ \lor $ ∼C, and from D, we get ∼B and ∼E. Combining these, we can infer that if A and D are true, then both B and E cannot be true simultaneously, leading to the conclusion that (A • D) ⊃ ∼(C $ \lor $ E) is derivable, as it captures the essence that if A and D are true, neither C nor E can be true to satisfy both original conditions.

1 a ⊃ (B ∨ \lor ∨ ∼C) 2 D ⊃ (∼B • ∼E) -Which of the Following

1 a ⊃ (B $\lor$ ∼C)
2 D ⊃ (∼B • ∼E)
-Which of the Following