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# Homework_1 - Homework 1 Math 139 Due Sep 7th Instructor...

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Unformatted text preview: Homework 1 - Math 139 Due Sep 7th Instructor Oﬃce Oﬃce hours Web page Mauro Maggioni 293 Physics Bldg. Monday 12pm-2pm. www.math.duke.edu/˜ mauro/teaching.html Reading: from Reed’s textbook: Chapter 1 Problems: §1.1: #3, 4, 7 §1.4: #1, 10 Additional Problems: 1. Let F be a ﬁeld. Using only the axioms (for a ﬁeld), prove that −ab = (−a)b for all a, b ∈ F . 2. Let P , Q and R be statements. Construct truth tables for the compound statements: P or (Q and R) and (P or Q) and (P or R) 3. Show that the two compound statements in 2. are equivalent: either both are true or both are false. 4. Choose statements P , Q and R and write the two corresponding (grammatically correct) English sentences. 5. Use truth tables to determine whether or not the following argument is correct: “If the tax rate and the unemployment rate both go up, then there will be a recession. If the GNP goes up, then there will not be a recession. The GNP and taxes are both going up. Therefore, the unemployment rate is not going up.” In other words, decide whether the concluding statement must be true, given that the preceding compound statements are true. 6. Do 5. without truth tables. ...
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