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)