You have a proof test on Wednesday. (See “Grading” tab for all the grading details.) To study, I suggest reviewing example proofs (we’ve done several in class now) by trying them yourself and them comparing to the author’s solutions. It’s ok for solutions to differ! Here are some exercises from Hammack that may be good (and have solutions in the back):

Use the definition of an “odd number” to be an integer of the form where is another integer. Show that if is odd, then is odd. The solution to this is written in great detail on pages 119-120 of Hammack.

Chapter 8, Exercise 1.

Chapter 7, Exercise 7. (This is an “if and only if” which means it goes both ways: if A then B and if B then A. Therefore we can state this as two theorems: Suppose . If then or . Furthermore, if or then . So it’s actually two review problems in one!

Examples 8.5, 8.6 on page 160. This uses the symbol for “divides” (Definition 4.4 on page 116).

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Try Hammack Exercises from Section 3.2, particularly 1, 3, 7, 9 (answers are in the back), more if you want more practice with the multiplication principle.