1. A ≡ ∼(B $ \lor $ C)
2. ∼D ≡ (A • E)
3. (D ⊃ B) • (E ⊃ B)
-Consider assuming 'B' 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) D
B) ∼D
C) E
D) ∼E
E) B $ \lor $ C

Question

Quizplus · Accepted Answer

Given the assumption of 'B' for conditional proof, the immediate consequence is 'B $ \lor $ C'. This follows directly because in propositional logic, if you have a proposition 'B', then 'B $ \lor $ C' is immediately true due to the disjunction introduction rule, which states that if you have a proposition, you can introduce a disjunction with any other proposition.

1 a ≡ ∼(B ∨ \lor ∨ C) 2 ∼D ≡ (A • E) 3

1 a ≡ ∼(B $\lor$ C)
2 ∼D ≡ (A • E)
3