Question

Select the conclusion that follows in a single step from the given premises. Throughout this test, write your answer on the form provided. Erasure marks may cause the grading machine to mark your answer wrong.

Given the following premises:
1. ∼N ∨ H
2. Q ⊃ ∼(∼N ∨ H)
3. (∼N ⊃ Q) • (H ⊃ Q)
Answer options:
A) Q ⊃ (N • ∼H) 2, DM
B) H ⊃ Q 3, Simp
C) ∼Q 1, 2, MT
D) ∼N ⊃ ∼(∼N ∨ H) 2, 3, HS
E) Q ∨ Q 1, 3, CD

Answer 1

The conclusion that follows in a single step from the given premises is H ⊃ Q.

Step-by-step explanation:

The correct answer is Option B) H ⊃ Q 3, Simp.

To identify the conclusion that follows in a single step from the given premises, we need to apply the rules of logical inference.

1. The first premise states that ∼N ∨ H.
2. The second premise states that Q ⊃ ∼(∼N ∨ H).
3. The third premise states that (∼N ⊃ Q) • (H ⊃ Q).

By applying the Simplification rule (Simp), we can deduce that H ⊃ Q is the conclusion that follows directly from the premises. Therefore, Option B is the correct answer.