Discussion Assignment

Discussion Assignment
CS 301k

Finish these problems before you attend discussion this week. For #1 and #2, you should write the claim in logical notation (define the universe and predicates), state the givens and goal, and show your scratch work.

1. Prove that the sum of any rational number and any irrational number is irrational.

2. Prove: For all integers a, b, and c, if a|b and a|c then a|(2b-3c).

3. What's wrong with the incorrect proof in #20 in the textbook on p. 123?

4. Draw a Venn diagram for these sets:
    a. (A-B) u C
    b. (A-B) u (B-A)

5. Write the definitions of the following sets using set-builder notation and interval notation. Recall that these are sets of real numbers, not integers.
    a. (-3, 20] u [-6, -2)
    b. (-3, 20] - [-6, -2)