Quiz 1

Show all work in a neat and organized fashion. Clearly indicate your answers.

10 points possible.

1. (2 pts.) Define the term prime. (Use the definition given in the textbook.)

2. (2 pts.) Define the term divisible. (Use the definition given in the textbook.)

3. (2 pts.) Let the set of natural numbers be the set of nonnegative integers; i.e., \Bbb N={0,1,2,3,...}. Use the concept of natural numbers to define the relation greater than or equal to ( ³ ) on the set of integers.

A correct answer begins: ``Let x and y be integers. We say that x is greater than or equal to y, and we write x ³ y, provided  ... .''

For this problem, you may freely use the operations (+, -, ×) on integers, but you must assume that the order relations ( < , £ , > , ³ ) are not yet defined on either natural numbers or integers.

4. (4 pts.) Suppose that x, y, and z are integers. Prove that if x | y and x | z, then x | (y+z).

Bonus. (1 optional bonus point possible) What are the two plurals of the word lemma ?