Question

 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 terms of C(x), D(x), F(x), quantifiers, and logical connectives. Let the domain consist of all students in your class. a) A student in your class has a cat, a dog, and a ferret. b) All students in your class have a cat, a dog, or a ferret. c) Some student in your class has a cat and a ferret, but not a dog. d) No student in your class has a cat, a dog, and a ferret. e) For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.

Answer 1

a) $\exist x:C(x)\land D(x)\land F(x)$

b) $\forall x:C(x)\lor D(x)\lor F(x)$

c) $\exist x: C(x)\land F(x)\land \neg D(x)$

d) $\nexists x:C(x)\land D(x)\land F(x)$

e) $\exists x \exists y \exists z:C(x)\land D(y) \land F(z)$