Question

Select the conclusion that follows in a single step from the given premises. Given the following premises:

1. E
2. R ⊃ ∼E
3. N ⊃ (∼C ⊃ R)
Select one:
a. ∼R 1, 2, MT
b. E • H 1, Add
c. ∼C ⊃ ∼E 2, 3, HS
d. E ⊃ ∼R 2, Trans
e. (N • ∼C) ⊃ R 3, Exp

Answer 1

The conclusion that follows in a single step from the given premises is ∼C ⊃ ∼E 2, 3, HS.

Step-by-step explanation:

The conclusion that follows in a single step from the given premises is option c. ∼C ⊃ ∼E 2, 3, HS.

1. Step 1: Apply the Hypothetical Syllogism (HS) rule by using premise 2 (R ⊃ ∼E) and premise 3 (N ⊃ (∼C ⊃ R)). By replacing R with ∼E from premise 2, we can infer ∼C ⊃ ∼E.