1. (A ⊃ B) • (C ⊃ D)
2. E ⊃ A
3. ∼F $ \lor $ E
4. ∼∼F
-Which of the following propositions is derivable from the given premises using the rules available through section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD)?
A) ∼A
B) B
C) ∼B
D) D ⊃ C
E) A ⊃ E

Question

Quizplus · Accepted Answer

From the premises, we can derive B using Modus Ponens (MP) and Hypothetical Syllogism (HS). Here's a brief explanation:1. From (4) ∼∼F, we can derive F using Double Negation (DN).2. From (3) ∼F $ \lor $ E and F, we can derive E using Disjunctive Syllogism (DS).3. From (2) E ⊃ A and E, we can derive A using Modus Ponens (MP).4. From (1) (A ⊃ B) • (C ⊃ D) and A, we can derive B using Modus Ponens (MP) again.

1 (A ⊃ B) • (C ⊃ D) 2 ∨ \lor ∨

1 (A ⊃ B) • (C ⊃ D)
2 $\lor$