Computer Science 260

Assignment 5

1. Give a proof by cases to prove that for all integers x, x

2 − x is an even integer.

2. Give a proof by contraposition that for a ∈ Z, if a

2 + 3 is odd, then a is even.

3. Give a proof by contradiction for real numbers a and b that a+b

2 < b ⇒ a < b.

4. Give a proof by contradiction that given integers j and k where j ≥ 2 that then

j 6 | k ∨ j 6 | (k + 1).