# Problem Set 1 Solution

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Problem 1. (2 points 5 = 10 points) Section 1.1, Exercise 8 on page 13.

Problem 2. (4 points 3 = 12 points) Section 1.1, Exercise 18 a), b), and c) on page 15. Explain. [Grading rubric: For each question, explanation 3 pts + true/false 1 pt]

Problem 3. (5 points 2 = 10 points) Section 1.1, Exercise 20 a) and c) on page 15. Explain. [Grading rubric: For each question, explanation 4 pts + true/false 1 pt]

Problem 4. (2 points 5 = 10 points) Section 1.1, Exercise 26 a), b), c), d), and e) on page 15.

Problem 5. (5 points 2 = 10 points) Section 1.1, Exercise 34 c) and d) on page 16.

Problem 6. (12 points) Section 1.2, Exercise 22 on page 24. Explain. [Grading rubric: Explanation 10 points + nal answer 2 points]

Problem 7. (12 points) Section 1.2, Exercise 24 on page 25. Explain. [Grading rubric: Explanation 10 points + nal answer 2 points]

Problem 8. (12 points) Section 1.3, Exercise 20 on page 38. Solve this problem by developing a series of logical equivalences, as shown in class and also in Examples 6 and 7 on pages 31{32. [Grading rubric: At least 6 derivation steps must be shown, and each derivation step must be accompanied by the (name of) law or logical equivalence used. Each step is worth 1pt (up to 6 pts), and explanation for each step worth 1 pt (up to 6 pts).]

Problem 9. (12 points) Section 1.3, Exercise 34 on page 38. Solve this problem by developing a series of logical equivalences, as shown in class and also in Example 8 on page 32. [Grading rubric: At least 8 derivation steps must be shown, and each derivation step must be accompanied by the (name of) law or logical equivalence used. Each step is worth 1pt (up to 8 pts) and explanation for each step worth 0.5 pts (up to 4 pts).]

Problem 10. (5 points 2 = 10 points) Section 1.4, Exercise 20 c) and d), page 57.

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