10. Let C(r) be the statement " has a cat," let D(z) be the statement " has a dog," and let F(x) be the statement " has a ferrett." 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. D (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.

An invalid argument is given below. 3X (P(x) v Q(x)) Vx P(x) (X)O XE : Suppose that the domain of x is the set {a, b}. Fill in the table values that prove that the argument is invalid. a Pick v Pick v Pick v 4 Check Next

Let P(x, y) be "x has taken class y," and Q(x, y) be "x has passed class y" and M(y) be "y is a math class," where the domain of x consists of all students in your class and the domain of y consists of all classes at LU. Use quantifiers to express this statement. (Assume that all email messages that were sent are received.) Every student in your class has passed a class at Liberty University that is not a math class.

Check if the following statement is TRUE or FALSE. Let p(x) and g(x) be two open predicates in a universe of discourse. Is it true that (x) (p(x) v g(x)) is equivalent to (Vxp(x)) v (Vxq(x))? O True O False