# Problem Set 2 Solution

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## Description

Problem 1. (5 points 2 = 10 points) Section 1.4, Exercise 36 b) and d), page 58.

Problem 2. (6 points 3 = 18 points) Section 1.5, Exercise 28 f), g), and i), page 71. Justify your answer or give a counterexample. [Grading rubric: For each subproblem, saying true / false correctly is 2 points and justifying your answer or giving a counterexample is worth 4 points.]

Problem 3. (10 points 2 = 20 points) Section 1.6, Exercise 14 c) and d), page 83.

Problem 4. (10 points) Section 1.7, Exercise 6, page 95.

Problem 5. (9 points 2 = 18 points) Section 1.7, Exercise 20, page 95.

Problem 6. (12 points) Prove by contradiction that if n 1 is a perfect square, then n + 2 is not a perfect square.

Problem 7. (12 points) Prove by contradiction that at least three of any 25 days chosen must fall in the same month of the year.

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