GATE 2003
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Question 32
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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)
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((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α⇒β]
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(∀x)[α] ⇒ (∃x)[α ∧ β]
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((∀x)[α ∨ β] ⇒ (∃x)[α] ⇒ (∀x)[α]
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(∀x)[α ⇒ β] ⇒ ((∀x)[α] ⇒ (∀x)[β])
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Question 32 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.
Correct Answer: D
Question 32 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.
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