Quiz 3 with Answers - Discrete Structures - 2003 | CMSC 250, Quizzes of Discrete Structures and Graph Theory

Download Quiz 3 with Answers - Discrete Structures - 2003 | CMSC 250 and more Quizzes Discrete Structures and Graph Theory in PDF only on Docsity! Name (printed): Student ID #: Section # (or TA’s: name and time) CMSC 250 Quiz ANSWERS #3 Wednesday, Sept. 17, 2003 1. [16 pnts.] For each of the following, tell the translation of that argument using the propositions given. Also, for each of the following identify the ONE rule being applied or tell that it is not one of those rules listed in your textbook and on the “cheat sheet”. Do not make any assumuptions about meaning (in other words, Assume “eating a certain fruit can make you feel hungry” and “if you feel hungry, you eat a certain fruit” are independent and both possible statements. ) Propositions: A=“Jan eats apples.”, M=“It is Monday.”, H=“Jan is hungry.” P=“Jan eats pears.” a. If Jan is hungry, she eats apples. H → A Jan doesn’t eat apples. ∼ A Jan is not hungry. ∼ H State the name of the rule that was applied here (or none): MT b. Jan eats apples or pears. A ∨ P If Jan eats apples, she is hungry. A → H If Jan eats pears, she is hungry. P → H Jan is hungry. H State the name of the rule that was applied here (or none): Dilemma c. Jan is hungry. H Either Jan is hungry or she eats apples. H ∨A Jan does not eat apples. ∼ A State the name of the rule that was applied here (or none): NONE d. Jan eats apples and pears. A ∧ P If today is Monday, then Jan eats apples. M → A Jan does not eat pears. ∼ P State the name of the rule that was applied here (or none): NONE Prove each of the arguments on the next page using only the rules from Chapter 1 (These are the same as the rules on the handout attached). Make sure you are using only those rules. For each line, make sure you tell the statement known to be true, the rule used to get that statement, and the line numbers to which the rule was applied to get that statement. ↓ TURN OVER ↓