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Final Exam Part 1 Ma 320-CRN 22189 Spring 2106 Carter General Instructions There are two parts to this exam. In the first part, I will ask you to define certain mathematical words and/or symbols. In the second part, you’ll use these terms to prove theorems. Don’t worry! After you turn in the first part, I’ll give you a sheet that reminds you of the definitions. Write your answers in complete sentences on another piece of paper. I am proud to have had you in my class, and I wish you the best for this test. Don’t underestimate the satisfying nature of a piece of cheese melted over a slice of bread. Define the italicized terms. 1. If d and n are integers and d 6= 0, define d|n that is d divides n. 2. The greatest common divisor gcd(a, b) of integers a, b. 3. A rational number. 4. The union, ∪, of two sets A and B. 5. The intersection, ∩, of two set A and B. 6. A relation between sets X and Y . f 7. A function Y ←− X. f 8. A function Y ←− X is injective or one-to-one. f 9. A function Y ←− X is surjective or onto. 10. The power set, P(X) of a set X. Please turn in this sheet, and receive the second section of the test. 1