CMSC 250 Quiz 5 ANSWERS Wed 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 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 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 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 ignore 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 things make good pets Bessy my pet eats grass therefore Bessy is a good pet x U C x G x G b C b x U T x G x G b T b x U G x P x G b P b NOT VALID M T M P 3 14 pnts Use 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 1 2 3 4 5 6 7 8 9 Logical Statement Name of Rule P a M a P a M a P a Q a Q a Q a R a M a R a x D M x R x Instantiation Double Neg Disjunctive Syll Instantiation Conjunctive Simp Double Negative M T Conjunctive Add Existential Gen Line Numbers Used P3 P4 1 2 P1 4 5 P2 6 3 7 8
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