Modus Ponens

Date: 07/10/2001 at 16:15:50
From: Erin Cushing
Subject: Math logic

This is my question: 

A man is x years old at the year x squared, and he was born in 1806.  
I am supposed to solve for x.  

I got the answer, 43, but I don't know how to explain it in terms of 
logic. When I asked my teacher, he said to use the Modus Ponens rule 
and I shouldn't have a problem, but I am.  

Please help me. Thank you.

Date: 07/10/2001 at 17:55:38
From: Doctor Jaffee
Subject: Re: Math logic

Hi Erin,

The Modus Ponens rule says that if you know that a statement, P, is 
true and that if P is true, then the statement Q is true, you can 
conclude that Q is true.

Your conclusion was that the man was 43 years old in 1849, so that 
must be the statement Q.  

Now, what is the mathematical relation between the year a person was 
born, the current year, and the the person's age?  If you can express 
that statement as an equation in terms of x, you will have the 
statement P.

Give it a try and if you want to check your solution with me, write 
back. If you are having difficulties, let me know and show me what you 
have done so far, and I'll try to help you some more.

Good luck.

- Doctor Jaffee, The Math Forum
  http://mathforum.org/dr.math/