CSPP 512 Mathematics for Computer Science - Summer 2001

Homework 5 (assigned July 16, due July 25)

This homework assignment covers the material in sections 1.6, 2.1, and 2.4 of the textbook.

1. Do problem 80 on page 63. (5 points)

2. Do problems 33, 42, 44, 47, 48, 50, 51, 54, 56, and 62 on pages 83-84. (Each problem is worth 3 points.)

3. Use mathematical induction to show that the statement below holds for all (positive) natural numbers n. This problem is worth 5 points.

   2n is less than or equal to 2ⁿ.

4. Use mathematical induction to show that the statement below holds for all (positive) natural numbers n. This problem is worth 5 points.

   1² + 2² + 3² + ... + n² = (1/6) n(n+1)(2n+1).

1. Prove that every number is either even or odd. (5 points)

2. Prove that if a set S of natural numbers contains n₀ and contains n+1 whenever it contains n, then S contains all natural numbers greater than or equal to n₀. (5 points)