By Alan Doerr, Kenneth Levasseur
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Additional resources for Applied Discrete Structures
7. All 15 players on the Tall U. basketball team are capable of playing any position. (a) How many ways can the coach at Tall U. fill the five starting positions in a game? (b) What is the answer if the center must be one of two players? 8. (a) How many ways can a gardener plant five diﬀerent species of shrubs in a circle? (b) What is the answer if two of the shrubs are the same? (c) What is the answer if all the shrubs are identical? 9. The president of the Math and Computer Club would like to arrange a meeting with six attendees, the president included.
B) If you are A and B’s mother? This problem is designed to show you that diﬀerent people can have diﬀerent correct answers to the same problem. 14. How many ways can a student do a ten-question true-false exam if he or she can choose not to answer any number of questions? 15. Suppose you have a choice of fish, lamb, or beef for a main course, a choice of peas or carrots for a vegetable, and a choice of pie, cake, or ice cream for dessert. If you must order one item from each category, how many diﬀerent dinners are possible?
This is an example of a proposition generated by p, q, and r. We will define this terminology later in the section. Since each of the three simple propositions has two possible truth values, it follows that there 46 CHAPTER 3. LOGIC are eight diﬀerent combinations of truth values that determine a value for c. These values can be obtained from a truth table for c. To construct the truth table, we build c from p, q, and r and from the logical operators. The result is the truth table below. Strictly speaking, the first three columns and the last column make up the truth table for c.
Applied Discrete Structures by Alan Doerr, Kenneth Levasseur