1. Define propositions P and Q and use them to give a real-world example of two fallacies we discussed (denying the hypothesis and affirming the conclusion).

Do the following problems using the formal proof techniques. Make sure:

• you begin by stating clearly what you are trying to prove
• you write the word "Proof"
• everything after that is a proposition
• each proposition is true (because it follows from prior steps and laws of logic; because it is a hypothesis; or because it is an assumption);
• each proposition has a number to its left
• each proposition has a justification (reason why it is true) to its right
• your final proposition is the proposition you are trying to prove
• you end with the words "QED"

Also, if you'tr trying to prove P-->Q, don't make the mistake of showing Q-->P