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

Given the following premises:
1.(C • ∼F) ⊃ E
2.G ∨ (C • ∼F)
3.∼(C • ∼F)a.
a. G ⊃ E 1, 2, HS
b. C 1, Simp
c. ~G 2, 3 DS
d. (G ∨ C) • ∼F 2, Assoc
e. C ⊃ (∼F ⊃ E) 1, Exp

1 Answer

3 votes

Final answer:

Using disjunctive syllogism, the conclusion that G must be true follows from the premises given, which means option c, ~G, is the correct conclusion.

Step-by-step explanation:

The question involves applying rules of logical inference to determine the correct conclusion from given premises.

The premises presented employ logical operators, and we must apply a correct form of reasoning to infer the conclusion.

When we consider premise 2, G ∨ (C • ¬F), and premise 3, ¬(C • ¬F), we can use the form of inference known as disjunctive syllogism.

This form allows us to deduce that if either G or (C • ¬F) must be true, and we know that (C • ¬F) is not true, then G must be true.

Thus, the correct conclusion that follows in a single step from the given premises is option a.

This is because based on the premises given and applying disjunctive syllogism, we deduce that G is true when ¬(C • ¬F) is also true.

Therefore, option c, ~G, can be selected correctly using disjunctive syllogism from premises 2 and 3.

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