Math Is Fun Forum

shaoen01

Member

Registered: 2008-01-26

Posts: 18

Fallacies in reasoning for modus ponens (method of affirming)

Hi everyone,

I have an invalid argument here, but i have difficulty determining if it is a converse or inverse error. It's hard for me to try to differentiate it at first glance, is there any technique in doing this right? Anyway, here is the argument:

Any sum of two rational numbers is rational
The sum r+s is rational
Therefore, the numbers r and s are both rational

Ans: Invalid argument, converse error.

My View:
By reading the above, i know it is wrong. But i can't explain it. Can someone maybe explain to me how it is a converse error? From my knowledge, a converse error is when:

p--> q
therefore, q
therefore, p

If someone can point to me which is p and q will be very helpful, thanks.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Fallacies in reasoning for modus ponens (method of affirming)

You are right that it is a converse error. The steps in the fallacy are:

where P is the statement “r and s are rational” and Q is the statement “r+s is rational”.

shaoen01

Member

Registered: 2008-01-26

Posts: 18

Re: Fallacies in reasoning for modus ponens (method of affirming)

Thanks for your reply, i just wanted to make sure i was right.