Math 230 Discrete Math Final Exam

Determine whether the argument is valid or if there is a fallacy in the argument: If n is a real number with n > 3, then n² > 9. Suppose that n² ≤ 9. Then n ≤ 3.

Valid argument using modus tollens

True or False?: If P = "2 + 1 = 3", then the negation of P is "2 × 1 ≠ 3".

False, the negation of P is "2 + 1 ≠ 3".

List the corresponding steps to prove
A− B⊆ A

1) Suppose x is in A - B
2) By definition, that means x is in A and not in B.
3) By simplification, that means x is in A.

Let the premises be the statements "Every student has an Internet account," "Homer does not have an Internet account," and  "Maggie has an Internet account."

The conclusion about Maggie is "Maggie is a student."

True or False?

False. There are no conclusions that can be drawn about Maggie.

Let the premises be the statements "All foods that are healthy to eat do not taste good," "Tofu is healthy to eat," "You only eat what tastes good," "You do not eat tofu," and Cheeseburgers are not healthy to eat."

The conclusion from the statements "For all x, if x is healthy to eat, then x does not taste good," "You only eat what tastes good," and "Cheeseburgers are not healthy to eat." is "Eat only cheeseburgers."

True or False?

False, there are no conclusions that can be drawn about cheeseburgers.

Let the argument be "Linda, a student in this class, owns a red convertible. Everyone who owns a red convertible has gotten at least one speeding ticket. Therefore, someone in this class has gotten a speeding ticket." 

c(x): x is in this class.

r(x): x owns a red convertible

t(x): x has gotten a speeding ticket.

The formal expression of the statement "Everyone who owns a red convertible has gotten at least one speeding ticket" is ∀x(t(x) → r(x)).

True or False?

False. The formal expression of the statement "Everyone who owns a red convertible has gotten at least one speeding ticket" is ∀ x(r(x) → t(x)).