• Nov 3rd 2008, 09:55 AM
ezwind72
Use a truth table to show that the argument given below (transitivity) is a valid argument form.

p→q
q→r
-----
∴ p→r

I am not 100% sure what I am supposed to be looking for, but I did construct the truth table. Does this look right?

Attachment 8531
• Nov 3rd 2008, 10:12 AM
Plato
No, that is not correct.
You need to add a column for $\left( {p \to q} \right) \wedge \left( {q \to r} \right)$.
Again add a column for $\left( {p \to q} \right) \wedge \left( {q \to r} \right)\to \left( {p \to r} \right)$.
• Nov 3rd 2008, 11:47 AM
ezwind72
Quote:

Originally Posted by Plato
No, that is not correct.
You need to add a column for $\left( {p \to q} \right) \wedge \left( {q \to r} \right)$.
Again add a column for $\left( {p \to q} \right) \wedge \left( {q \to r} \right)\to \left( {p \to r} \right)$.

Why do I need to and them? And when it is all said and done, I want to see that I have a tautology?