SampleFinalExam

SampleFinalExam - MATH M118: Finite Mathematics Practice...

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MATH M118: Finite Mathematics Practice Department Final Examination 1. Write the following argument in symbolic notation. Then construct a truth table and determine whether the argument is valid or not. If it rains, then the crops will grow. It did not rain. Therefore, the crops did not grow. Use p: It rains. q: The crops will grow. 2. Complete the following truth table. p q q p ) ( q p ¬ ) ( q p p ¬ T T T F F T F F 3. Complete the following truth table. p q p ¬ q p ¬ ) ( q p q ¬ T T T F F T F F 4. Let p denote the statement “Jack gets a job,” and q denote the statement “Jack buys a new car.” Write each of the following compound statements using symbolic notation. a. Jack did not get a job but he bought a new car. b. If Jack gets a job, then he will buy a new car. c. Jack did not get a job or buy a new car. d. The contrapositive of the statement in 4b.
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5. Let U = {1, 2, 3, … , 10, 11, 12}. Let X, Y and Z be subsets of U such that X = {2, 4, 6, 8, 10} Y= {4, 5, 6, 7, 8} Z = {5, 6, 9, 10} a. Find (X – Y) U Z b. Find X Z 6. Determine if each of the following statements is true (always true) or false (not always true): a. U B B = b. A A U = c. H G H G = ) ( d. F E F E = 7. Of the 200 students who participated in a survey, 105 like pizza, 75 like tacos and 42 like both. How many like neither? Draw a Venn diagram for this problem. 8. A group consists of 10 men and 11 women. In how many ways can a team of exactly 4 men and 6 women be selected? 9. A car show has 22 cars competing for "Best in Show." Prizes are awarded for first, second and third place; any one car may only win one prize. In how many ways can the prizes be awarded? 10. How many different committees of 3 can be formed from 15 Republicans and 12 Democrats if at least one Republican and at least one Democrat must be on the committee? Circle the correct set up. a. P(15,3) P(12,3) b. C(15,3) C(12,3) c. P(15,1)P(12,2) + P(15,2) P(12,1) d. C(15,1)C(12,2) + C(15,2) C(12,1) e. 1 - P(15,3) P(12,3) f. 1 - C(15,3) C(12,3)
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11. How many three-digit even numbers can be formed using digits from the set {1, 2, 3, 4, 5, 6, 7} a. If no digit can be repeated in any one number? b. If digits can be repeated? 12. An urn contains 5 purple, 6 orange, and 3 black marbles. In how many ways can 3 marbles be selected, without replacement, so that at least one of the three is black? 13. A group of people composed of 6 men and 3 women is to randomly select a committee of 3 people. Find the probability that all 3 are men. 14. At Dee Dee's Dinette the probability that a customer orders coffee is 0.60, the probability that a customer orders pie is 0.35, and the probability that a customer orders neither coffee nor pie is 0.30. Find the probability that a customer orders both coffee and pie. 15.
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This note was uploaded on 04/28/2008 for the course MATH 118 taught by Professor All during the Spring '08 term at IUPUI.

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SampleFinalExam - MATH M118: Finite Mathematics Practice...

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