Which of the following is a valid first order formula? (Here α and β are first…

2003

Answer: D. (∀x)[α ⇒ β] ⇒ ((∀x)[α] ⇒ (∀x)[β]) — A valid first-order formula must follow proper logical syntax and quantifier rules. Option (D): (∀x)[α⇒β]⇒((∀x)[α]⇒(∀x)[β]) is a well-formed first-order…

1. A.

   {[(∀x)[α] ⇒ (∀x)[β]] ⇒ [(∀x)[α ⇒ β]]}

2. B.

   (∀x)[α] ⇒ (∃x)[α ∧ β]

3. C.

   {[(∀x)[α ∨ β]] ⇒ [(∃x)[α] ⇒ (∀x)[α]]}

4. D.

   (∀x)[α ⇒ β] ⇒ ((∀x)[α] ⇒ (∀x)[β])

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