Unformatted text preview: Homework 1 - Math 139
Due Sep 7th Instructor
Web page Mauro Maggioni
293 Physics Bldg.
www.math.duke.edu/˜ mauro/teaching.html Reading: from Reed’s textbook: Chapter 1
Problems: §1.1: #3, 4, 7 §1.4: #1, 10
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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