2. Let C(r) be the statement has a cat, and let D(r) be the statement...

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2. Let C(r) be the statement " has a cat," and let D(r) be the statement " has a dog." Let the domain consist of all students in this class. (i) Express each of the following sentences in terms of C(r), D(z), quantifiers, and logical connectives. (a) Every student in this class has both a cat and a dog. (b) Some student in this class has a dog but not a cat. (c) No student in this class has both a cat and a dog. (d) Every student in this class who does not have a cat has a dog. (ii) Express each of the following propositions in regular sentences. (a) Vr(C(r) → D(x)) (b) Vr(D(x)→→C(x)) (c) (3xC(x)) ^ (VxD(x)) (d) Vr(C(r) D(x)) 2. Let C(r) be the statement " has a cat," and let D(r) be the statement " has a dog." Let the domain consist of all students in this class. (i) Express each of the following sentences in terms of C(r), D(z), quantifiers, and logical connectives. (a) Every student in this class has both a cat and a dog. (b) Some student in this class has a dog but not a cat. (c) No student in this class has both a cat and a dog. (d) Every student in this class who does not have a cat has a dog. (ii) Express each of the following propositions in regular sentences. (a) Vr(C(r) → D(x)) (b) Vr(D(x)→→C(x)) (c) (3xC(x)) ^ (VxD(x)) (d) Vr(C(r) D(x))

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a Every student in this class has both a cat and a dog rCr Dr b S... View the full answer