Transcript Slide 1
Intro to Logic Theory Statement - Intro to Logic Theory Statement – A sentence that is either true or false, but not both simultaneously Intro to Logic Theory Statement – A sentence that is either true or false, but not both simultaneously Truth Value – Intro to Logic Theory Statement – A sentence that is either true or false, but not both simultaneously Truth Value – The truth or falsity of a statement Intro to Logic Theory Statement – A sentence that is either true or false, but not both simultaneously Examples of Statements E-mail is a way to communicate Intro to Logic Theory Statement – A sentence that is either true or false, but not both simultaneously Examples of Statements E-mail is a way to communicate Newton is the capitol of New Jersey Intro to Logic Theory Statement – A sentence that is either true or false, but not both simultaneously Examples of Statements E-mail is a way to communicate Newton is the capitol of New Jersey 6+5>4 Intro to Logic Theory Statement – A sentence that is either true or false, but not both simultaneously Examples of Statements E-mail is a way to communicate Newton is the capitol of New Jersey 6+5>4 11+6=12 Intro to Logic Theory The following examples are NOT statements Intro to Logic Theory The following examples are NOT statements Access the file Intro to Logic Theory The following examples are NOT statements Access the file Is this a great country or what? Intro to Logic Theory The following examples are NOT statements Access the file Is this a great country or what? A-Rod is better than Derek Jeter Intro to Logic Theory The following examples are NOT statements Access the file Is this a great country or what? A-Rod is better than Derek Jeter This sentence is false Intro to Logic Theory The following examples are NOT statements Access the file Is this a great country or what? A-Rod is better than Derek Jeter This sentence is false 4+5+6 Intro to Logic Theory Compound Statement - Intro to Logic Theory Compound Statement - A sentence that is comprised of two or more statements. The statements are connected by such words as “or” “and” “not” “if…then” Intro to Logic Theory Examples of Compound Statements Intro to Logic Theory Examples of Compound Statements Shakespeare wrote sonnets and the poem has 5 verses Intro to Logic Theory Examples of Compound Statements Shakespeare wrote sonnets and the poem has 5 verses You can pay me now or you can pay me later Intro to Logic Theory Examples of Compound Statements Shakespeare wrote sonnets and the poem has 5 verses You can pay me now or you can pay me later If he said it, then it must be true Intro to Logic Theory Examples of Compound Statements Shakespeare wrote sonnets and the poem has 5 verses You can pay me now or you can pay me later If he said it, then it must be true The statement – “My pistol was made by Smith and Wesson” is NOT a compound statement because in this case, the word and is not used as a statement connector Intro to Logic Theory Negation – A statement that is formed by making an alteration to a given statement, which makes a true statement false, or a false statement true. Intro to Logic Theory Write the negation of each statement Intro to Logic Theory Write the negation of each statement I do not like green eggs and ham Intro to Logic Theory Write the negation of each statement I do not like green eggs and ham I do like green eggs and ham Intro to Logic Theory Write the negation of each statement It is going to snow Intro to Logic Theory Write the negation of each statement It is going to snow It is not going to snow Intro to Logic Theory Write the negation of each statement Pluto is not a planet Intro to Logic Theory Write the negation of each statement Pluto is not a planet Pluto is a planet Intro to Logic Theory Write the negation of each statement Gil Hodges will be in the Hall of Fame Intro to Logic Theory Write the negation of each statement Gil Hodges will be in the Hall of Fame Gill Hodges will not be in the Hall of Fame Intro to Logic Theory Write the negation of each statement x 4 y 5 Intro to Logic Theory Write the negation of each statement x 4 y 5 x 4 y 5 Intro to Logic Theory Quantifiers – Words that make a generalized statement Intro to Logic Theory Quantifiers – Words that make a generalized statement Some common quantifiers are all, some none Intro to Logic Theory Examples of quantified statements All dogs are bad Some guys have all the luck None of these batteries are worth the money Intro to Logic Theory Writing the negation of a quantified statement requires some thought Intro to Logic Theory Writing the negation of a quantified statement requires some thought All dogs are bad Intro to Logic Theory Writing the negation of a quantified statement requires some thought All dogs are bad Not all dogs are bad Intro to Logic Theory Writing the negation of a quantified statement requires some thought All dogs are bad Not all dogs are bad Some dogs are not bad Intro to Logic Theory Writing the negation of a quantified statement requires some thought All dogs are bad Not all dogs are bad Some dogs are not bad Notice that if the initial statement is true, then the negation must be false, and vice versa Intro to Logic Theory Writing the negation of a quantified statement requires some thought All dogs are bad Is the statement Some dogs are bad a negation? Intro to Logic Theory Writing the negation of a quantified statement requires some thought All dogs are bad Is the statement Some dogs are bad a negation? No, because BOTH statements can be either true or false simultaneously. Intro to Logic Theory A statement and its negation MUST ALWAYS have opposite truth values Intro to Logic Theory Write the negation of each statement Some guys have all the fame Intro to Logic Theory Write the negation of each statement Some guys have all the fame No guys have all the fame Intro to Logic Theory Write the negation of each statement Every dog has its day Intro to Logic Theory Write the negation of each statement Every dog has its day Not every dog has its day Intro to Logic Theory Write the negation of each statement All dogs have their day Intro to Logic Theory Write the negation of each statement All dogs have their day Not all dogs have their day At least one dog does not have its day Intro to Logic Theory Write the negation of each statement All dogs have their day No dogs have their day is NOT a proper negation because if one dog has its day and another dog doesn’t have its day, then BOTH the statement and its negation would be FALSE Intro to Logic Theory Write the negation of each statement Some dogs have their day Intro to Logic Theory Write the negation of each statement Some dogs have their day No dogs have their day Intro to Logic Theory Write the negation of each statement No dogs had their day Intro to Logic Theory Write the negation of each statement No dogs had their day Some dogs had their day At least one dog had its day Intro to Logic Theory Write the negation of each statement No dogs had their day Can we say “All dogs had their day” is a negation of the statement above? Homework, pg 99-100 #1-32 Decide whether each of the following is a statement or is not a statement, 1. December 7, 1941, was a Sunday. 2. The ZIP code for Manistee, MI, is 49660. 3. Listen, my children, and you shall hear of the mid-night ride of Paul Revere. 4. Yield to oncoming traffic. 5. 5 + 8 = 13 and 4 - 3 =1 Homework, pg 99-100 #1-32 Decide whether each of the following is a statement or is not a statement, 1. December 7, 1941, was a Sunday. Yes 2. The ZIP code for Manistee, MI, is 49660. Yes 3. Listen, my children, and you shall hear of the mid-night ride of Paul Revere. No 4. Yield to oncoming traffic. No 5. 5 + 8 = 13 and 4 - 3 =1 Yes Homework, pg 99-100 #1-32 Decide whether each of the following is a statement or is not a statement, 6. 5 + 8 = 12 or 4 — 3 = 2 7. Some numbers are negative. 8. Andrew Johnson was president of the United States in 1867. 9. Accidents are the main cause of deaths of children under the age of 8. 10. Star Wars: Episode I—The Phantom Menace was the top-grossing movie of 1999. Homework, pg 99-100 #1-32 Decide whether each of the following is a statement or is not a statement, 6. 5 + 8 = 12 or 4 — 3 = 2 Yes 7. Some numbers are negative. Yes 8. Andrew Johnson was president of the United States in 1867. Yes 9. Accidents are the main cause of deaths of children under the age of 8. Yes 10. Star Wars: Episode I—The Phantom Menace was the top-grossing movie of 1999. Yes Homework, pg 99-100 #1-32 Decide whether each of the following is a statement or is not a statement, 11. Where are you going today? 12. Behave yourself and sit down. 13. Kevin “Catfish” McCarthy once took a prolonged continuous shower for 340 hours, 40 minutes. 14. One gallon of milk weighs more than 4 pounds. Homework, pg 99-100 #1-32 Decide whether each of the following is a statement or is not a statement, 11. Where are you going today? No 12. Behave yourself and sit down. No 13. Kevin “Catfish” McCarthy once took a prolonged continuous shower for 340 hours, 40 minutes. Yes 14. One gallon of milk weighs more than 4 pounds. Yes Homework, pg 99-100 #1-32 Decide whether each of the following statements is compound. 15. 1 read the Chicago Tribune and I read the New York Times. 16. My brother got married in London. 17. Tomorrow is Sunday. 18. Dara Lanier is younger than 29 years of age, and so is Teri Orr. Homework, pg 99-100 #1-32 Decide whether each of the following statements is compound. 15. 1 read the Chicago Tribune and I read the New York Times. Yes 16. My brother got married in London. No 17. Tomorrow is Sunday. No 18. Dara Lanier is younger than 29 years of age, and so is Teri Orr. Yes Homework, pg 99-100 #1-32 Decide whether each of the following statements is compound. 19. Jay Beckenstein’s wife loves Ben and Jerry’s ice cream. 20. The sign on the back of the car read “California or bust!” 21. If Julie Ward sells her quota, then Bill Leonard will be happy. 22. If Mike is a politician, then Jerry is a crook. Homework, pg 99-100 #1-32 Decide whether each of the following statements is compound. 19. Jay Beckenstein’s wife loves Ben and Jerry’s ice cream. No 20. The sign on the back of the car read “California or bust!” No 21. If Julie Ward sells her quota, then Bill Leonard will be happy. Yes 22. If Mike is a politician, then Jerry is a crook. Yes Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 23. Her aunt’s name is Lucia. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 23. Her aunt’s name is Lucia. Her aunt’s name is not Lucia Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 24. The flowers are to be watered. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 24. The flowers are to be watered. The flowers are not to be watered Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 25. Every dog has its day. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 25. Every dog has its day. Not every dog has its day Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 26. No rain fell in southern California today. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 26. No rain fell in southern California today. Some rain fell in southern California today. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 27. Some books are longer than this book. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 27. Some books are longer than this book. No books are longer than this book. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 28. All students present will get another chance. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 28. All students present will get another chance. Not all students present will get another chance. Some students present will not get another chance At least one student present will not get another chance Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 29. No computer repairman can play blackjack. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 29. No computer repairman can play blackjack. Some computer repairmen can play blackjack At least one computer repairman can play blackjack. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 30. Some people have all the luck. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 30. Some people have all the luck. No people have all the luck. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 31. Everybody loves somebody sometime. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 31. Everybody loves somebody sometime. Not everybody loves somebody At least one person does not love somebody Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 32. Everyone loves a winner. Homework, pg 99-100 #1-32 Write a negation for each of the following statements. 32. Everyone loves a winner. Not everyone loves a winner. Some people do not love a winner. At least one person does not love a winner. If you are having some difficulty, see me for extra help, or….. If you are having some difficulty, see me for extra help, or….. You can get assistance from someone who is VERY smart…… Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following ~p Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following ~p The costumes are not scary Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following ~q Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following ~q The weather is not warm Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following pq Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following pq The costumes are scary and the weather is warm Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following pq Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following pq The costumes are scary or the weather is warm Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following ~ pq Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following ~ pq The costumes are not scary or the weather is warm Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following p ~ q Symbols in Logic Theory Let p represent the statement “The costumes are scary” and Let q represent the statement “The weather is warm” Write a statement to represent the following p ~ q The costumes are scary and the weather is not warm Conjunction AND 3 2 5 3 26 3 2 5 and 3 2 6 T T T 3 2 5 3 25 3 2 5 and 3 2 5 T 3 2 6 F 3 26 F 3 2 6 and 3 2 6 F T F 3 2 6 F 3 25 F 3 2 6 and 3 2 5 F Disjunction OR 3 2 5 T 3 26 T 3 2 5 or 3 2 6 T 3 2 5 3 25 3 2 5 or 3 2 5 T 3 2 6 F 3 26 T 3 2 6 or 3 2 6 F T T 3 2 6 F 3 25 F 3 2 6 or 3 2 5 F