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Computer Science 260 Assignment 5

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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).

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