Chapter 17
Homework 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 Microsoft^TM 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.