## Chapter 17Homework for the fourth week: symbolic logic

### 17.1 Homework

Practice is absolutely critical in this class.

Groups are fine, turn in your own work. Homework is due in or before class on Mondays.

• Section 3.1
• Problems 1-5
• Problems 40, 42, 44
• Problems 49-54
• Section 3.2
• Problems 15-18
• Problems 37-40
• Problems 53-55
• Problems 61, 62
• Section 3.3
• Problems 1-5
• Problems 13, 15, 20
• Problems 35-38
• Problems 58, 60
• Problems 67, 68
• Problems 74, 75
• Section 3.4
• Problems 1, 3, 6
• Problem 51, 57, 58
• Section 3.1 again
• Problems 55, 56
• Problems 60-64
• Problem 75
• Problem 76. Hint: Quantifiers do not necessarily exclude each other.
• Negate the following, and decide if the statements are true or false.
• There is a number p for all numbers q such that the difference between p and q is 2.
• For all sets A, for all sets B, there is a set C such that A ∩ B = C and C is not .
• Derive a logic expression from the following truth table. Attempt to simplify it remembering the distributive property, De Morgan’s laws, and that \mathrel{⊧}z ∨\mathop{¬}z ≡ 1 and \mathrel{⊧}z ∧\mathop{¬}z ≡ 0.

 p q r f(p,q,r) 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0
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• Section 3.6: Delayed until after the test week.
• Problems 3, 6
• Problems 17, 19, 21
• Problems 47, 49
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Note that you may email homework. However, I don’t use MicrosoftTM products (e.g. Word), and software packages are notoriously finicky about translating mathematics.

If you’re typing it (which I advise just for practice in whatever tools you use), you likely want to turn in a printout. If you do want to email your submission, please produce a PDF or PostScript document.