Question 3471 – Mathematical-Reasoning
February 28, 2024Question 10427 – Deadlock
February 29, 2024Question 9610 – Propositional-Logic
Which of the following is a valid first order formula? (Here α and β are first order formulae with x as their only free variable)
Correct Answer: D
Question 12 Explanation:
Option D is valid.
Here, α, β are holding values of x. Then and RHS saying that α holding the value of x and β is holding value of x.
Then LHS ⇒ RHS.
Here, α, β are holding values of x. Then and RHS saying that α holding the value of x and β is holding value of x.
Then LHS ⇒ RHS.
((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α⇒β]
(∀x)[α] ⇒ (∃x)[α ∧ β]
((∀x)[α ∨ β] ⇒ (∃x)[α] ⇒ (∀x)[α]
(∀x)[α ⇒ β] ⇒ ((∀x)[α] ⇒ (∀x)[β])
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