# Homework Assignment #2

#### Due on paper in lecture, Wednesday 15 February 2011.

There are twelve questions for 60 total points plus 10 extra credit. All but one are from the textbook, Mathematical Foundation for Computer Science. Note that the book has both Exercises and Problems -- make sure you are doing a Problem and not the Exercise with the same number. The number in parentheses following each problem is its individual point value.

Correction in purple made on 4 February 2012.

• Problem 1.7.2 (5) (You must find and justify expressions using → and ¬ that are equivalent to x ∧ y, x ∨ y, x ⊕ y, and x ↔ y.)

• Problem 1.8.2 (5)

• Problem B-1 (10): Given the premise (x ⊕ y) ∧ (z ∨ x), give a deductive sequence proof of the compound proposition y → (¬x ∧ z). Then, from the same premise, give a separate deductive sequence proof of the compound proposition ¬z → x. The first conclusion was originally given as y → (x ∧ ¬z).

• Problem 1.10.4 (5)

• Problem 1.10.5 (10 extra credit)

• Excursion 1.11, Writing Exercise #2 (5)

• Problem 2.3.2 (5)

• Excursion 2.4, Writing Exercise #1 (5)

• Problem 2.5.4 (5)

• Problem 2.6.2 (5)

• Problem 2.8.1 (5)

• Problem 2.9.2 (5) (Don't bother with the "explain carefully" part.)