Consider the following argument with premise \(({\forall _x}P\left( x \right)) \vee Q\left( x \right))\) and conclusion \(({\forall _x}P\left( x \right)) \wedge (\forall_xQ\left( x \right))\)(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)

• A. This is a valid argument.
• B. Steps (C) and (E) are not correct inferences
• C. Steps (D) and (F) are not correct inferences
• D. Step (G) is not a correct inference