Question 3. 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". Match the following quantified statements with their English translations. No justification necessary. Assume that the universe of discourse consist of all students in 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 this 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 one of these animals. (1) Vx (C(x) V D(x) V F(x)) (II) 3x (C(x) A F(x) ^-D(x)) (III) (3x C(x)) ^ (3x D(x)) ^ (3x F(x)) (IV) 3x (C(x) A D(x) ^ F(x)) (V) 3x (C(x) A D(x) ^ F(x)) A
Question 3. 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". Match the following quantified statements with their English translations. No justification necessary. Assume that the universe of discourse consist of all students in 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 this 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 one of these animals. (1) Vx (C(x) V D(x) V F(x)) (II) 3x (C(x) A F(x) ^-D(x)) (III) (3x C(x)) ^ (3x D(x)) ^ (3x F(x)) (IV) 3x (C(x) A D(x) ^ F(x)) (V) 3x (C(x) A D(x) ^ F(x)) A
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 3. 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". Match the following quantified statements with their English translations.
No justification necessary. Assume that the universe of discourse consist of all students in 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 this 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 one of
these animals.
(I) Vx (C(x) V D(x) v F(x))
(II) 3x (C(x) ^ F(x) ^ ¬D(x))
(III) (3x C(x)) ^ (3x D(x)) ^ (3x F(x))
(IV) 3x (C(x) A D(x) ^ F(x))
(V) x (C(x) ^ D(x) ^ F(x))
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