Assignment I

Due date Sep. 16.

1. From text: exercises 0.1, 0.2.

2. Prove that the sum of the cubes of the integers from 1 to N = N^2 (N+1)^2 / 4,

where "^" denotes exponentiation.

3. Review the definition of relation (p. 8). Consider the following relation on the integers:

R = {(x, y) | x in N and y in N and x+y is even}

in words: R is a binary relation on the integers, and two numbers are said to be in this relation if their sum is a multiple of two.

Prove or disprove: R is an equivalence relation.