Homework #2, Due Wenesday, November 9, in class.

1. What is wrong with the following proof?

    Theorem: If n^2 is positive, then n is positive.

    Proof: Suppose that n^2 is positive. Because the implication is true, we can conclude that n is positive.

2, What is wrong with the following argument (which purports to show that n is an even integer whenever n^2 is an even integer): Suppose that n^2 is even. Then n^2=2k for some integer k. Let n=2m for some integer m. This shows that n is even.

3. Prove that m^2=n^2 iff m=n or m=-n.

Section 2.1. #12
Section 2.2. #8, 12
Section 2.3. #8
Section 2.4. #14
Section 2.5, #6, 8 10, 12, 14, 16, 18, 20

Section 3.1. #6
Section 3.2. #8. 16