# DISCRETE MATH: Determine whether an argument is correct or not

1. Homework Statement

Determine whether the argument is correct or incorrect and explain why.

A) Everyone enrolled in the university has lived in a dormitory. Mis has never lived in a dormitory. Therefore, Mia is not enrolled in the university.

B) A convertible car is fun to drive. Isaac's car is not a convertible. Therefore, Isaac's car is not fun to drive.

C) Quincy likes all action movies. Quincy likes the movie Eight Men Out. Therefore, Eight Men Out is an action movie.

D) All lobstermen set at least a dozen traps. Hamilton is a lobsterman. Therefore, Hamilton sets at least a dozen traps.

2. Homework Equations

Modus Tollens:

$$\neg\,q$$
$$p\,\longrightarrow\,q$$
----------
$$\therefore\,\neg\,p$$

Modus Ponens:

$$p$$
$$p\,\longrightarrow\,q$$
----------
$$\therefore\,q$$

Fallacey of denying the hypothesis.

3. The Attempt at a Solution

A) E(x) = "x is enrolled in the university" and L(x) = "x has lived in a dormitory"

$$\neg\,L(Mia)$$
$$E(x)\,\longrightarrow\,L(x)$$
----------
$$\therefore\,\neg\,E(Mia)$$

Argument is correct, it uses Modus Tollens.

B) C(x) = "x is a convertible" and F(x) = "x is fun to drive"

$$\neg\,C(Isaac's\,\,car)$$
$$C(x)\,\longrightarrow\,F(x)$$
----------
$$\therefore\,\neg\,F(Isaac's car)$$

Argument is invalid, fallacey of denying the hypothesis.

C) I don't know how to set this one up, can some one help? I think it is invalid because of Fallacey of Affirming the conclusion, is that right?

D) L(x) = "x is a lobsterman" and T(x) = "x sets at elast a dozen traps"

$$L(Hamilton)$$
$$L(x)\,\longrightarrow\,T(x)$$
----------
$$\therefore\,T(Hamilton)$$

Argument is correct, it uses Modus Ponens.