Question

Select the conclusion that follows in a single step from the given premises. Be careful not to skip steps.

1. Q ⊃ (H • ∼F)
2. ∼(Q • ∼M)
3. ∼G ⊃ (Q • ∼M)
A) ∼QV∼∼M 2,DM
B) G∨∼(Q⋅M) 2,Add
C) Q⊃∼(∼H∨F) 2,DM
D) G 2,3,MT
E) Q 2,Simp
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Answer 1

The conclusion that directly follows from the premises using valid deductive reasoning is D) G, achieved through Modus Tollens.

Step-by-step explanation:

The objective is to select the conclusion that follows in a single step from the given premises without skipping steps. Given the rules of deductive reasoning and valid deductive inferences, we can analyze each potential conclusion:

• A) ¬Q V ¬¬M 2, DM - This applies De Morgan's rule to the second premise but does not follow as a direct single step.
• B) G V ¬(Q ⋅ M) 2, Add - This option uses Addition, which is not a direct inference from the premises given.
• C) Q ⊃ ¬(¬H V F) 2, DM - Here, De Morgan's rule is being applied incorrectly as it's not a single step inference from the premises.
• D) G 2,3, MT - Modus Tollens (MT) can be used here because if ¬G then Q ⋅ ¬M, but we're given ¬(Q ⋅ ¬M), thus G can be directly inferred.
• E) Q 2, Simp - Simplification cannot directly infer Q from ¬(Q ⋅ ¬M).

Hence, the correct answer is D) G 2,3, MT, which matches the valid argument structure of Modus Tollens.