(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 movieEight Men Out. Therefore,Eight Men Outis 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. Relevant equations

Modus Tollens:

[tex]\neg\,q[/tex]

[tex]p\,\longrightarrow\,q[/tex]

----------

[tex]\therefore\,\neg\,p[/tex]

Modus Ponens:

[tex]p[/tex]

[tex]p\,\longrightarrow\,q[/tex]

----------

[tex]\therefore\,q[/tex]

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"

[tex]\neg\,L(Mia)[/tex]

[tex]E(x)\,\longrightarrow\,L(x)[/tex]

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[tex]\therefore\,\neg\,E(Mia)[/tex]

Argument is correct, it uses Modus Tollens.

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

[tex]\neg\,C(Isaac's\,\,car)[/tex]

[tex]C(x)\,\longrightarrow\,F(x)[/tex]

----------

[tex]\therefore\,\neg\,F(Isaac's car)[/tex]

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"

[tex]L(Hamilton)[/tex]

[tex]L(x)\,\longrightarrow\,T(x)[/tex]

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[tex]\therefore\,T(Hamilton)[/tex]

Argument is correct, it uses Modus Ponens.

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

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