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 "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.

Answer 1

Answer and Step-by-step explanation:

C(x) be the statement "x has a cat"

D(x) be the statement "x has a dog"

F(x) be the statement "x has a ferret".

Universe = x = all students in your class.

a) A student in your class has a cat, a dog and a ferret   = ∃x(C(x) ∧ D(x) ∧ F(x))

b) All students in your class have a cat, a dog, or a ferret  =  ∀x(C(x) ∨ D(x) ∨ F(x))

c) Some students in your class has a cat and a ferret but not a dog  = ∃x (C(x) ∧ F(x) ∧ ¬D(x))

d) No student in this class has a cat, a dog and a ferret  ¬∃x (C(x) ∧ D(x) ∧ F(x))

e) For each of the three animals, cats, dogs and ferrets, there is as student in your class who has one of the three animals.  (∃xC(x)) ∧ (∃xD(x)) ∧ (∃xF(x))