HW #1

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.

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;
         you must also explain how they support your answer.