Homework for the fourth week: symbolic logic

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 - Section 3.6: Delayed until after the test week.
- Problems 3, 6
- Problems 17, 19, 21
- Problems 47, 49

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.