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Let P (x) be the statement "has been to Prague", where the domain consists of your classmates.
- Express each of these quantifcations in English.
- ∃x :(P (x))
- ∀x :(P (x))
- ¬∃x :(P (x))
- ¬∀x :(P (x))
- ∃x :(¬P (x))
- ∀x :(¬P (x))
- ¬∃x :(¬P (x))
- ¬∀x :(¬P (x))
- Which of these mean the same thing?
Let C (x) be the statement "x has a cat", let D (x) be the statement "x has a dog", and let F (x) be the statement "x has a ferret". Express each of these statements in first-order logic using these relations. Let the domain be your classmates.
- A classmate has a cat, a dog, and a ferret.
- All your classmates have a cat, a dog, or a ferret.
- At least one of your classmates has a cat and a ferret, but not a dog.
- None of your classmates has a cat, a dog, and a ferret.
- For each of the three animals, there is a classmate of yours that has one.
Determine the truth value of each of these statements if the domain is all real numbers. Where appropriate, give a witness.
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