Name printed Student ID Section or TA s name and time CMSC 250 Quiz 5 Wednesday Feb 25 2004 Write all answers legibly in the space provided The number of points possible for each question is indicated in square brackets the total number of points on the quiz is 30 and you will have exactly 15 minutes to complete this quiz You may not use calculators textbooks or any other aids during this quiz 1 10 pnts Use an Euler diagram to determine if each of the following represents a valid argument Make sure to label the parts of the diagram If the argument is invalid you must have the Euler diagram represent that fact If the argument is valid just draw one of the Euler diagrams which show a valid interpretation Only cats are nice Some cats are yellow therefore Some yellow things are nice Circle One Valid Invalid Some people are frightened things All frightened things act strange therefore All people act strange Circle One Valid Invalid TURN OVER 2 6 pnts Translate the individual statements into symbolic notation in the first available column and then write either M P or M T or instantiation to tell which rule was used to reach the conclusion shown or say that the argument is not valid by any of these in the second available column You must use the Universe of all things as your domain for any quantified variables you may use b as a name instantiation to represent Bessy and you may use without indication any double negation considerations Predicates C x x is a cow G x x eats grass T x x is a tiger and P x x is a good pet a b c All cows eat grass Bessy my pet eats grass therefore Bessy is a cow No tigers eat grass Bessy my pet eats grass therefore Bessy is not a tiger All grass eating animals make good pets Bessy my pet eats grass therefore Bessy is a good pet 3 14 pnts Using only the rules provided on the handout of the Logical Equivalence Rules and the Rules of Inference to prove the following It is a Valid Argument you need to prove it without using a truth table P1 P2 P3 P4 x D P x Q x y D R y Q y z D P z M z P a where a D therefore x D M x R x Line Logical Statement 1 2 3 4 5 6 7 8 9 10 11 12 Name of Rule Line Numbers Used
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