Consider the argument with premise ∀x(P(x) ∨ Q(x)) and conclusion (∀x P(x)) ∧ (∀x Q(x)): (A) ∀x(P(x) ∨ Q(x)) premise; (B) P(c) ∨ Q(c) universal instantiation from A; (C) P(c) simplification from B; (D) ∀x P(x) universal generalization of C; (E) Q(c) simplification from B; (F) ∀x Q(x) universal generalization of E; (G) (∀x P(x)) ∧ (∀x Q(x)) conjunction of D and F.

1. AThis is a valid argument
2. BSteps (C) and (E) are not correct inferences
3. CSteps (D) and (F) are not correct inferences
4. DStep (G) is not a correct inference

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: B. Steps (C) and (E) are not correct inferences

Explanation

Simplification applies to a conjunction, not a disjunction: from P(c) ∨ Q(c) you cannot infer P(c) or Q(c). Steps C and E are invalid.