CORRECT ANSWER is option2Explanation:For C and E to be true, the assertion should be P(c) ∧ Q(c). Hence, this is not a correct inferenceIn predicate logic, universal generalization STATES that if ⊢ P ( x ) {\displaystyle \vdash \!P(x)} has been derived, then ⊢ ∀ x P ( x ) {\displaystyle \vdash \!\forall x\,P(x)} can be derived.

"> CORRECT ANSWER is option2Explanation:For C and E to be true, the assertion should be P(c) ∧ Q(c). Hence, this is not a correct inferenceIn predicate logic, universal generalization STATES that if ⊢ P ( x ) {\displaystyle \vdash \!P(x)} has been derived, then ⊢ ∀ x P ( x ) {\displaystyle \vdash \!\forall x\,P(x)} can be derived.

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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)

Logical and Verbal Reasoning Logic in Logical and Verbal Reasoning 1 year ago

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The CORRECT ANSWER is option2Explanation:For C and E to be true, the assertion should be P(c) ∧ Q(c). Hence, this is not a correct inferenceIn predicate logic, universal generalization STATES that if ⊢ P ( x ) {\displaystyle \vdash \!P(x)} has been derived, then ⊢ ∀ x P ( x ) {\displaystyle \vdash \!\forall x\,P(x)} can be derived.

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