Discrete Structures

# HW #1

 Last Update: 12 January 2009 Note: or material is highlighted

All exercises are from §1.1 (propositional logic).

Each HW problem's solution should consist of:

• a restatement of the entire problem (you may copy it word for word),
• followed by a complete solution with all intermediate steps shown.

 PUT YOUR NAME, DATE, & RECITATION SECTION AT TOP RIGHT OF EACH PAGE; STAPLE MULTIPLE PAGES

1. p. 17: 10d

2. p. 18: 20a, b, c, d, g

• Note: For problem 20, you may have to rewrite some of the English phrases as grammatically correct, full sentences.

E.g., "To be a citizen..." is not a full sentence, but it can be rewritten as "Someone is a citizen..." or as "You are a citizen...", etc.

3. p. 19: 30d

• Note: For this problem, be sure to show each "intermediate" column of the truth table.

4. p. 19: 42

5. pp. 19-20: 44

• Note: For problems 42 and 44, besides answering each question with "yes", "no", "maybe", "I don't know", etc., you must also say why that's your answer!

6. p. 20: 52

• Suggestion:

• Choose proposition letters for each atomic proposition.
• Then represent each compound proposition in the language of propositional logic.
• Is there an assignment of truth values that will make all 5 propositions true?

• If so, what is it?
• If not, why not?

• Alternatively, construct truth tables for the sentences.

• Use the truth tables to help answer the question.
• But don't just show the truth tables;