# t31fa02 - COT3100.01 Fall 2002 Final Exam(Test#3 Print Name...

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COT3100.01, Fall 2002 Final Exam (Test #3) Print Name: ____________________________ S. Lang (12/03/2002) Social Security No.: __________________ Instruction: The test is a closed-book, closed-notes, and no-calculator test. The test has 6 pages (double-sided), 11 questions, and 100 total points. The last two sheets (3 pages) contain the relevant definitions, formulas, and theorems from the notes, which you can tear off and use for reference. In writing your proofs, you need to show all the steps, and explain each by using the appropriate definition or theorem, by either stating the name, stating the actual contents, or giving its reference number as shown on the reference sheet. Your signature below indicates you have read and understood this instruction. Signature: ______________________________________ Part I. (36 pts., 3 pts. each) True/False, or short-answer, questions. (No explanation needed and no partial credit given.) 1. Let A = {1, 2, 3, 4} and let R A × A denote a binary relation depicted by the directed graph given in the figure. Answer each of the following True/False questions: 2. Define two real-valued functions f : [0, ) R and g : R R by the following formulas, where the set [0, ) denotes the set of non-negative real numbers, and R denotes the set of all real numbers, f ( x ) = x - 1, and g ( x ) = 2 x + 1. Answer the following questions:

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t31fa02 - COT3100.01 Fall 2002 Final Exam(Test#3 Print Name...

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