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Let C(a) be the statement "a has a cat", let D(x) be the statement "a has a dog" and let F(x) be the statement "arhas a ferret". Express each of the following statements in terms of C(x), D(z), and F(x), quantifiers, and logical connectives. Let the universe of discourse consist of all students in your class. Put the appropriate letter next to the corresponding symbolic form. 1. Ba(C(2) A D(z) A F(x)) 2. -Jæ(C(2) A D(x) A F(x)) 3. 3r(C(x)) A (3rD(x)) A (3F(x)) 4. 3r(C(x) A F(x) A -D(2)) 5. Va(C(r) V D(r) V F(æ)) 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.

Let C(a) be the statement "a has a cat", let D(x) be the statement "a has a dog" and let F(x) be the statement "arhas a ferret". Express each of the following statements in terms of C(x), D(z), and F(x), quantifiers, and logical connectives. Let the universe of discourse consist of all students in your class. Put the appropriate letter next to the corresponding symbolic form. 1. Ba(C(2) A D(z) A F(x)) 2. -Jæ(C(2) A D(x) A F(x)) 3. 3r(C(x)) A (3rD(x)) A (3F(x)) 4. 3r(C(x) A F(x) A -D(2)) 5. Va(C(r) V D(r) V F(æ)) 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.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 29E
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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 "xhas a ferret". Express each of the following statements in terms of C(x), D(x), and F(x), quantifiers, and logical connectives. Let the universe of discourse consist of all students in your class. Put the appropriate letter next to the corresponding symbolic form. 1. Ja(C(x) A D(x) ^ F(x)) 2. ¬3æ(C(x) ^ D(x) ^ F(x)) 3. Jæ(C(x)) A (JaD(x)) ^ (JaF(x)) 4. Jæ(C(x) ^ F(x) ^ ¬D(x)) 5. Væ(C(x) V D(x) V F(x)) 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.
Transcribed Image Text: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 "xhas a ferret". Express each of the following statements in terms of C(x), D(x), and F(x), quantifiers, and logical connectives. Let the universe of discourse consist of all students in your class. Put the appropriate letter next to the corresponding symbolic form. 1. Ja(C(x) A D(x) ^ F(x)) 2. ¬3æ(C(x) ^ D(x) ^ F(x)) 3. Jæ(C(x)) A (JaD(x)) ^ (JaF(x)) 4. Jæ(C(x) ^ F(x) ^ ¬D(x)) 5. Væ(C(x) V D(x) V F(x)) 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.
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