# valid statement or not?

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• Jun 24th 2007, 11:59 AM
TheRekz
valid statement or not?
I have to determine whether the statement below is valid or not:

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

My answer is that according to modus tollens this statement is valid. Is this right?

p -> q
~q
-------
~p
• Jun 24th 2007, 12:14 PM
Jhevon
Quote:

Originally Posted by TheRekz
I have to determine whether the statement below is valid or not:

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

My answer is that according to modus tollens this statement is valid. Is this right?

p -> q
~q
-------
~p

it's been a while since I did logic (an introductory course), so let's see. if "therefore" can be translated as "this implies" then the statement is valid. otherwise, i don't think so.

remember that $P \implies Q \Longleftrightarrow \left( \sim Q \right) \implies \left( \sim P \right)$

• Jun 24th 2007, 12:32 PM
TheRekz
so my answer is correct right by saying that this is valid, but i have to change

~p->~q
~q
-------
therefore ~p is true

right??
• Jun 24th 2007, 12:35 PM
Jhevon
Quote:

Originally Posted by TheRekz
so my answer is correct right by saying that this is valid, but i have to change

~p->~q
~q
-------
therefore ~p is true

right??

yes, i would say so. if th implication is true and the last statement is true, then the first one must be true for the implication to be true. there was one other thing bothering me though

EDIT: no it should be ~q -> ~p
• Jun 24th 2007, 12:44 PM
Ilaggoodly
i would not interpret it as an if and only if, id sa its (P->Q) ->(~P->~Q) which is not a valid statement. And if you think about it intuitively, just because a car isnt a convertibe does not mean it cant be fun to drive, it would be valid to say if its not fun to drive then its not a convertible, which is contraposition
• Jun 24th 2007, 12:45 PM
TheRekz
sorry for the typo! thanks

and I have one more question that I am not sure of,

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

This statement is not valid right? It's some kind of fallacy affirming the conclusion.
• Jun 24th 2007, 12:49 PM
TheRekz
Quote:

Originally Posted by Ilaggoodly
i would not interpret it as an if and only if, id sa its (P->Q) ->(~P->~Q) which is not a valid statement. And if you think about it intuitively, just because a car isnt a convertibe does not mean it cant be fun to drive, it would be valid to say if its not fun to drive then its not a convertible, which is contraposition

so you mean that this is an invalid statement? If I think about it intuitively, your point makes sense. But how do I proof it using logical statements.
• Jun 24th 2007, 12:54 PM
Jhevon
Quote:

Originally Posted by Ilaggoodly
i would not interpret it as an if and only if, id sa its (P->Q) ->(~P->~Q) which is not a valid statement. And if you think about it intuitively, just because a car isnt a convertibe does not mean it cant be fun to drive, it would be valid to say if its not fun to drive then its not a convertible, which is contraposition

that was the problem i had with the statement. there could be other types of cars that are fun to drive as well, and Isaac's car could be one of those.

i used if and only if because the statements are equivalent, not because i was interpreting the question like that i should have said maybe, $P \implies Q \equiv \sim Q \implies \sim P$
• Jun 24th 2007, 12:56 PM
Jhevon
Quote:

Originally Posted by TheRekz
sorry for the typo! thanks

and I have one more question that I am not sure of,

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

This statement is not valid right? It's some kind of fallacy affirming the conclusion.

right, we have the same situation here. what if Quincy also likes all comedies (which they neglected to tell us) and Eight Men out was a comedy, then Quincy would like it, even though it's not an action movie. so we see that the statement is invalid
• Jun 24th 2007, 12:56 PM
TheRekz
well I think that this statement can be converted to p-->q because it says nothing about if and only if
• Jun 24th 2007, 12:59 PM
Jhevon
Quote:

Originally Posted by TheRekz
well I think that this statement can be converted to p-->q because it says nothing about if and only if

yes, "only" is the word missing that would make these statements valid. if they had said, "only convertibles are fun to drive" and "Quincy only likes action movies" then the two statements would be valid
• Jun 24th 2007, 01:11 PM
Plato
Quote:

Originally Posted by TheRekz
A convertible car is fun to drive. Isaac's car is not a convertible. Therefore, Isaac's car is not fun to drive.

First my I suggest that you use letters that have something to do with the statements. C is convertible; F is fund to drive.
Now the argument is:
$\begin{array}{l}
C \Rightarrow F \\
\sim C \\
\therefore \sim F \\
\end{array}$

Clearly that is an invalid argument.
The is the fallacy of denying the hypotheses.

May I also suggest that if we are not sure of the question, please wait to answer.
• Jun 24th 2007, 01:15 PM
Jhevon
Quote:

Originally Posted by Plato
First my I suggest that you use letters that have something to do with the statements. C is convertible; F is fund to drive.
Now the argument is:
$\begin{array}{l}
C \Rightarrow F \\
\sim C \\
\therefore \sim F \\
\end{array}$

Clearly that is an invalid argument.
The is the fallacy of denying the hypotheses.

I see. It's all so simple now :D you are the man, Plato!

Quote:

May I also suggest that if we are not sure of the question, please wait to answer.
Yes sir. Boredom makes you jumpy i guess
• Jun 24th 2007, 01:21 PM
TheRekz
Quote:

Originally Posted by Plato
First my I suggest that you use letters that have something to do with the statements. C is convertible; F is fund to drive.
Now the argument is:
$\begin{array}{l}
C \Rightarrow F \\
\sim C \\
\therefore \sim F \\
\end{array}$

Clearly that is an invalid argument.
The is the fallacy of denying the hypotheses.

May I also suggest that if we are not sure of the question, please wait to answer.

thanks plato that clears up!
• Jun 24th 2007, 02:21 PM
Soroban
Hello, TheRekz!

\
Quote:

Determine whether the argument below is valid or not:

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

My answer is that according to modus tollens this statement is valid. Is this right?

p -> q
~q
-------
~p

. . . sorry, no

Let $p: \text{ the car is a convertible}$
Let $q: \text{ the car is fun to drive}$

"A convertible car is fun to drive"
. . If the car is a convertible, then the car is fun to drive": . $p \rightarrow q$

"Isaac's car is not a convertible": . $\sim p$

Therefore, "Isaac's car is not fun to drive": . $\sim q$

The arguement has the form: . $\begin{array}{c}p \rightarrow q \\ \sim p \\ ---- \\
\therefore \;\sim q \end{array}$

Not valid . . . fallacy of the inverse.

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