1.1 Intro to Proofs

Let \(P\) be a proposition, \(Q\) be another proposition.

1. What is a proposition of the form \(\text{IF } P, \text{ THEN } Q \) called?

   Exercise 1

     implication , 'if and only if conclusion consequent None of the above implication 
   \(\text{IF } P, \text{ THEN } Q \) is the general form of an implication and is often written as \(P \text{ IMPLIES } Q\). Thus, given specific \(P\) and \(Q\), \(P \text{ IMPLIES } Q\) is itself a proposition and can be either true or false.

2. A fundamental inference rule says:

   \(\dfrac{P,\;\; P \text{ IMPLIES } Q}{Q}\).

   1. What is this inference rule called?

      Exercise 2

        The Fundamental Inference Rule Modus Ponens The Fundamental Rule of Logic None of the above Modus Ponens 
      
      

   2. What is the statement above the line called?

      Exercise 3

        numerator antecedent all of the above None of the above antecedent 
      
      

   3. What is the statement below the line called?

      Exercise 4

        conclusion consequent all of the above None of the above all of the above 
   Review Chapter 1.4.1.

3. Proving a proposition's contrapositive is as good as (and sometimes easier than) proving the proposition itself. Which of the following is logically equivalent to the contrapositive of \(P \text{ IMPLIES } Q\)?

   Exercise 5

     NOT(P IMPLIES Q) NOT(P) IMPLIES NOT(Q) NOT(Q) IMPLIES NOT(P) None of the above NOT(Q) IMPLIES NOT(P) 
   Draw a Venn diagram with \(P\) inside of \(Q\).

4. At the end of a proof, it is customary to write down either the delimiter _____ or the symbol _____.

   Exercise 6

     Done, \(\Diamond \) QED, \(\Diamond \) END, \(\Box \) QED, \(\Box \) QED, \(\Box \) 
   A proof should begin with "Proof by ..." and end with "QED" or \(\Box \).
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