MGF1106 Review Chapter 8 NAME Date Time 1 Negate the statement in words and write the negation symbolically 4 2 7 or 3 5 15 p q It is not true that 4 2 7 or 3 5 15 q p q p 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 a musician and he is not a poet q p q p 3 Using DeMorgan s Laws write a sentence that is equivalent to the following It is not true that she is not a musician or he is a poet p q p q She is a musician and he is not a poet 4 q p p p q T T F F T F T F q F T F T p q p q p p F F T T F F F T F F T T 5 Find the truth value of the statement if p and q are false and r is true p q p r 5 False T T F F T F F 6 Construct a truth table and determine if the statement is a tautology p q r p not a tautology Form B p q r T T T T F F T T F F T T T F T F T F q F F T T F F p q F F T T F F 1 13 2019 p F F F F T T r p F T F T T T p q r p T T F T T T F F Form B F F T F T T F F 1 13 2019 T T T T T T 7 Write the direct statement in if then form then using symbols write the converse inverse and contrapositive Direct f No mammals have feathers If it is a mammal then it has no feathers Converse f m Inverse m m f Contrapositive f m 8 Explain why the following statement is true or false A week has eight days if and only if December has 31 days It is false because both statements do not have the same truth value 9 Rewrite the following statements in if then form words a Informed voting v is sufficient to being a good citizen c v c If you are an informed voter then you are a good citizen b Reading the newspaper n is necessary to being an informed voter v v n If you are an informed voter then you read the newspaper 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 I do not go to Office Depot therefore my printer does not run out of ink p q p q Contrapositive reasoning p q q p 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 did not get my work done then the dogs are not happy p q q r p r misuse of transitive reasoning Invalid Form B 1 13 2019 Valid p q q r p r Class Practice 3 1 28 p The U S is the country with the most internet users r It is not true that Michael is the most common boys name not comprehensive Express s q NJ is a planet s The final exam was The final exam was comprehensive 30 All journalists are writers a Equivalent statement There are no journalists who are not writers b Negation Some journalists are not writers 36 No women have served as Supreme Court justices a Equivalent statement All women have not served as Supreme Court Justices b Negation Some women have served as Supreme Court justices 38 President Nixon assured the American people that In all my years of public service I have never obstructed justice Later events indicated that he was not telling the truth Therefore in his years of public service a Nixon always obstructed justice b Nixon sometimes did not obstruct justice c Nixon sometimes obstructed justice d Nixon never obstructed justice 3 2 Pg 102 24 p The heater is working q The house is cold Express p q The heater is not working if and only if the house is cold 32 q It s the July 4th r We are having a barbecue Express q r It s July 4th if and only if we re not having a barbecue 38 p Romeo loves Juliet q Juliet loves Romeo Express p q It is not true that Romeo loves Juliet or that Juliet loves Romeo 48 p The temperature outside is freezing q The heater is working r The house is cold Express in symbolic form If the heater is working then the temperature outside is freezing if and only if the house is cold q p r p The temperature is above 85 q We finished studying r We go to the beach 56 Express p r q If the temperature is not above 85 then we do not go to the beach or we finished studying 62 Express p q r finished studying then we Form B If is not true that the temperature is above 85 and we do not go to the beach 1 13 2019