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GATE | GATE-CS-2017 (Set 1) | Question 22
Consider the first-order logic sentence
F: ∀ x (∃ y R(x,y)).
Assuming non-empty logical domains, which of the sentences below are implied by F?
I. ∃y (∃x R(x,y))
II. ∃y (∀x R(x,y))
III. ∀y (∃x R(x,y))
IV. ∼∃x (∀y R(x,y))
F: ∀ x (∃ y R(x,y)).
Assuming non-empty logical domains, which of the sentences below are implied by F?
I. ∃y (∃x R(x,y))
II. ∃y (∀x R(x,y))
III. ∀y (∃x R(x,y))
IV. ∼∃x (∀y R(x,y))
(A)
IV only
(B)
I and IV only
(C)
II only
(D)
II and III only
Answer
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