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Consider the following sentence:
“There is exactly one God”
Let G(x) : x is a God
Now consider the following predicate logic statements.
I. ∃ × God⁡(x)
II. ∃ × God⁡(x) ∧∀y (God(y) ⇒ x = y))
III. ∃ x ∀y(God⁡(x) ∧ (∼ God⁡(y) ∨ x =y))
The number of statements which are equivalent to the above sentence is ________.
Correct answer is '2'. Can you explain this answer?
Verified Answer
Consider the following sentence:“There is exactly one God”Let G(x) : ...
* I is not correct because it says "at least one God" instead of "exactly one God”.
* II is clearly the correct statement.
* III is same as II and can be obtained using,
p ⇒ q ≡ ∼ p ∨ q
\)God\y) \Rightarrow(x = y \equiv(\sim \operatorname{God}(y) \vee x = y\)
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Consider the following sentence:“There is exactly one God”Let G(x) : x is a GodNow consider the following predicate logic statements.I. ∃ × God⁡(x)II. ∃ × God⁡(x) ∧∀y (God(y) ⇒ x = y))III. ∃ x ∀y(God⁡(x) ∧ (∼ God⁡(y) ∨ x =y))The number of statements which are equivalent to the above sentence is ________.Correct answer is '2'. Can you explain this answer?
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