MGF1106 Review Chapter 8 9 2 NAME 1 Negate the statement in words and write the negation symbolically Heller wrote Catch 22 and Shakespeare wrote Hamletp q It is not true that Heller wrote Catch 22 and Shakespeare wrote Hamlet p q p q For 2 and 3 let p represent She is a musician and q represent He is a poet 2 Translate the following compound statements into symbols It is not true that she is not a musician or he is a poet p q p q 3 Using DeMorgan s Laws write a sentence in words that is equivalent to the following It is not true that she is a musician and he is not a poet p q p q She is not a musician or he is a poet 4 p q p p q T T F F T F T F q F T F T q p T T F T p p q p F F T T F F F T 5 Find the truth value of the statement if p and r are false and q is true p q p r 5 True T F F T F F T 6 Construct a truth table and determine if the statement is a tautology p q r p Not a tautology Form A p q r p T T T T F F F F T T F F T T F F T F T F T F T F F F F F T T T T q F F T T F F T T p q F F F F F F T T 1 14 2019 r F T F T F T F T r p p q r p T T T T T F T F T T T T T T T F 7 Write the direct statement in if then form words then using symbols write the converse inverse and contrapositive All integers are rational numbers If it is an integer then it is a rational number i r Converse r i Inverse i r Contrapositive r i 8 Explain why the following statement is true or false A week has eight days if and only if December has 40 days It is true because both statements are false and a biconditional is true only when both simple statements have the same truth value 9 Rewrite the following statements in if then form words a Informed voting v is necessary to being a good citizen c c v If you are a good citizen then you are an informed voter b Reading the newspaper n is sufficient to being an informed voter v n v If you read the newspaper then you will be an informed voter Determine whether the following arguments are valid or invalid Be sure to support your answer 10 If my printer runs out of ink then I go to Office Depot p q My printer does not run out of ink p therefore I do not go to Office Depot q p q p q Fallacy of the inverse 11 If I get my work done then I can play with the dogs If I play with the dogs then they will be happy therefore if I get my work done the dogs will be happy p q q r p r transitive reasoning Form A 1 14 2019 Invalid p q q r p r Valid Sections 9 1 9 2 12 Insert the appropriate symbol a a a b c d e f b q a b c d e f d b d f a b c d e f c a c g a b c d e f 13 How many subsets can be found in A a b c d e f 64 26 13 14 Let U a b c d e f g B a b e f C a c d e g a B C B C a b e f b f b f b A B A B U The employees in one section of a electric utility company cut down tall trees climb poles and splice wire The section chief reported the following information to management Of the 100 employees in the section 45 can cut tall trees T 50 can climb poles P 57 can splice wire W 28 can cut trees and climb poles 20 can climb poles and splice wire 25 can cut trees and splice wire 11 can do all three How many can t do any of the three 15 Draw a Venn diagram showing the numbers in each region Use the diagram template above Trees 3 14 Wire 23 11 17 9 13 Poles 10 16 How many people can only climb poles 13 16 17 How many people can do none of these 10 17 18 How many people can cut trees and climb poles but can t splice wire 18 17 Form A 1 14 2019