# Truth Tables

• Dec 18th 2010, 02:19 PM
Herricane
Truth Tables
The Problem

Write a truth table for the following to figure out if the argument is valid

jane and Pete both won't win the math prize
Pete will win either the math prize or chemistry prize
Jane will win the math prize
Therefore Pete will win the chemistry prize

I know it is a valid argument but I am not sure how to start.
This is what I have:

Jane wins the math prize - J
Pete wins the math prize - P
Do I also have to include one for chemistry?

How do I write out the Premise? Is it just J or P (exclusive or)
• Dec 18th 2010, 02:27 PM
snowtea
JM - Jane wins math prize
PM - Pete wins math prize
JC - Jane wins chem
PC - Pete wins chem

Construct a 2^4 = 16 row truth table with all possible values of JM PM JC PC

The first 3 statements are assumptions (respectively they are):
not(JM and PM)
PM or PC
JM

The statement you are trying to prove is
PC

Proving this by the truth table amounts to checking that for every row where all the assumptions are true, the value of PC is true.

Note: You can simplify your truth table by only looking at values of JM = true since that is one of your assumptions.
• Dec 18th 2010, 02:31 PM
Herricane
Thank you. Now I understand it better.