COP 3100 Intro to Discrete Structures Lab 01 Dr Sahar Hooshmand sahar hooshmand ucf edu Department of Computer Science Question 1 Translate the following statement into propositional logic using the propositions provided You are eligible to be President of the U S A only if you are at least 35 years old were born in the U S A or at the time of your birth both of your parents were citizens And also you have lived at least 14 years in the country Express your answer using e You are eligible to be President of the U S A a You are at least 35 years old b You were born in the U S A p At the time of your birth both of your parents were citizens r You have lived at least 14 years in the country 2 Solution Translate the following statement into propositional logic using the propositions provided You are eligible to be President of the U S A only if you are at least 35 years old were born in the U S A or at the time of your birth both of your parents were citizens And also you have lived at least 14 years in the country Express your answer using e You are eligible to be President of the U S A a You are at least 35 years old b You were born in the U S A p At the time of your birth both of your parents were citizens r You have lived at least 14 years in the country Solution e a b p r 3 Question 2 n Using a truth table show that always have the same value You just proved something What is it 4 Solution T T T T F F F F T T F F T T F F T F T F T F T F T T F F F F F F T F F F T F F F T F F F F F F F T F F F F F F F This proves that conjunction is associative T T T T T T T T 5 Question 3 n Use a truth table to show that p q r and p q p r are logically equivalent 6 Solution 7 Question 4 n Let p q and r be the propositions p You have the flu q You miss the final exam r You pass the course Express each of the following propositions as an English sentence a p q b q r c q r d p q q r 8 Solution n Let p q and r be the propositions p You have the flu q You miss the final exam r You pass the course Express each of the following propositions as an English sentence a p q If you have the flu then you will miss the final exam or You will miss the final exam if you have the flu b q r You pass the course if and only if you do not miss the final exam c q r If you miss the final exam then you will not pass the course d p q q r Either you have the flu and miss the final exam or you don t miss the final exam and pass the course 9 Question 5 n Using a truth table show that 10 Solution 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 F F T T F F T T F T F T F T F T T T F F F F F F T F T T T T T T F F T T T T T T T F T T T T T T 11
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