
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)

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.

Thank you. Now I understand it better.