Propositions and Logic Senior High School General Mathematics.pptx

Logic and Argument for grade 11 mathematics

1. My son always tells the truth Propositions and Symbols KINEAH RUZIL SANDY S. MEDIONA ^ v Teacher I ~ My Father is a liar p q

2. My son always tells the truth ^ v ~ My Father is a liar p q Propositions and Logical Statements

3. My son always tells the truth ^ v ~ My Father is a liar p q Who tells the truth?

4. My son always tells the truth ^ v ~ My Father is a liar p q Learning Competency: Illustrate Propositions A 1 B Differentiate Statements Define Propositions; Illustrate Propositions Objectives:

5. My son always tells the truth ^ v ~ My Father is a liar p q Activity/Drill You are the love of my life Identify what kind of Statements are in the following items 1 Declarative Are you Gay? Run! Zaldy Run! Today is Thrusday Who is the Guilty in the Flood Control Corruption? Interrogative Imperative Declarative Interrogative

6. My son always tells the truth ^ v ~ My Father is a liar p q Activity/Drill You are the love of my life Among the statements which of the following can be either TRUE or FALSE? 1 Declarative Are you Gay? Run! Zaldy Run! Today is Thrusday Who is the Guilty in the Flood Control Corruption? Interrogative Imperative Declarative Interrogative Declarative

7. My son always tells the truth ^ v ~ My Father is a liar p q Propositions Propositions are statements whose Truthfulness and Falsity can by Verified or Justified 1 Today is Monday Duterte kill drug pushers and addict during Tokhang Marcos Jr. ‘s Presedency is the Golden Era of Good Governance The House of Representatives are to be blame for the Flood Control Corruption

8. My son always tells the truth ^ v ~ My Father is a liar p q Propositions Propositions are statements whose Truthfulness and Falsity can by Verified or Justified 1 Try Making your Own Illustration of A Proposition/ Propositional Statement How to Verify the Truthfulness of a Proposition?

9. My son always tells the truth ^ v ~ My Father is a liar p q Propositions Propositions are statements whose Truthfulness and Falsity can by Verified or Justified 1 How to Verify the Truthfulness of a Proposition? The Truth Value of a Proposition can be verified using Known Facts, Standards and Premises

10. My son always tells the truth ^ v ~ My Father is a liar p q Propositions Propositions are statements whose Truthfulness and Falsity can by Verified or Justified 1 Example 1. The Sea is salty 2. Vegetables are Healthy The Truth fullness of these Propositions can be Verified through known facts about the subjects

11. My son always tells the truth ^ v ~ My Father is a liar p q Propositions Propositions are statements whose Truthfulness and Falsity can by Verified or Justified 1 Example 1. I love you 2. Ang totoong Iglesia ay ang Iglesia ni Cristo 3. The Saturday is the 7 th Day of the Week which is the Sabbath Day The Truth fullness of these Propositions can be Verified through Standards (Opinions)

12. My son always tells the truth ^ v ~ My Father is a liar p q Quiz Illustrate the Proposition. Determine whether the following are proposition. Determine how to Verify the truthfulness of a Proposition 1 Today is Sunny Day Is the Class Suspended? Are you Okey? You will get colds when you go in the rain without covering your head Get you ID! Now !

13. My son always tells the truth ^ v ~ My Father is a liar p q Learning Competency: Symbolize Proposition A 1 B Symbolizes Propositions Combine Simple Proposition Symbolizes Propositional Statements Objectives: Distinguish Simple and Compound Propositions B

14. My son always tells the truth ^ v ~ My Father is a liar p q Activity/Drill Plants Produce their food through the process of Photosynthesis Determine if the statements are Propositions and the Verification/Justification of its Truth 1 Bathing in sunshine every morning produces Vitamin D for the Body Does the Sun also revolve to a certain heavenly body? Please be Quiet. Love!

15. My son always tells the truth ^ v ~ My Father is a liar p q Paradox PARADOX are statements whose Truthfulness and Falsity cannot be Verified or Justified thus are NOT propositions. 1 This statement is false If you travel back in time and Prevent your Grandfather from having children you cannot exist. The universe is vast , extraterrestrial civilization should exist A plate that is about to fall in a closed cupboard is both intact and also broken at the same time.

16. My son always tells the truth ^ v ~ My Father is a liar p q Symbolism in Proposition Propositions are symbolized using a first letter of the main thought of the proposition. 1 Arnold is a Working Student the proposition can be Symbolized as “ A ” or “ W ”. General symbols can also represent the proposition “ P ”, “ Q ” and “ R ”

17. My son always tells the truth ^ v ~ My Father is a liar p q Symbolism in Proposition Propositions are symbolized using a first letter of the main thought of the proposition. 1 It is a Cloudy Today the proposition can be Symbolized as “ C ” Monkey Eats Banana the proposition can be Symbolized as “ M ”or “ B ”

18. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 CONJUNCTION simple propositions connected using the word “ and ” and symbolized as “ ^ ” R: Roses are Red S: The Sky is Blue Roses are Red and the Sky is Blue “R ^ S”

19. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 CONJUNCTION “ but ” can also use instead of and if the propositions are opposite in nature. R: I love you S: I lie I Love you but I lie “U ^ L”

20. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 DISJUNCTION are simple propositions that are connected using the word “ or ” and symbolled as “ v ” . M: He watches a movie D: He dines with his friends (Either) he watches a movie or dines with his friends “M v D”

21. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 S: I Study well E: I will pass the Exam If I study well then I will pass the exam Conditional are simple propositions that are connected using the word “ if ” …..“ then ” it is represented as p q “S D”

22. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 Conditional are simple propositions that are connected using the word “ if ” …..“ then ” it is represented as p q S: I Study well E: I will pass the Exam If I study well then I will pass the exam “S D”

23. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 Antecedent and Consequent The Antecedent (Hypothesis) is the ‘’ P ” statement and Consequent (Conclusion) is the “ Q ” in the p q If I study well then I will pass the exam Antecedent Conclusion

24. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 NEGATION The negation of a given statement is a statement that is flase whanever the given statement is true and true whenever the given statement is false “ ~ ” P : I will pass the Exam ~P : I will not pass the exam / I will fail the Exam

25. My son always tells the truth ^ v ~ My Father is a liar p q Activity Determine if it simple or compound Proposition 1 Bamboo are Grass I win or I Lose I work efficiently but it makes me tired If it rains then the road is wet Sarah loves Curlee

26. My son always tells the truth ^ v ~ My Father is a liar p q Activity Symbolized the following Propositions 1 Bamboo are Grass I win or I Lose I work efficiently but it makes me tired If it rains then the road is wet Sarah loves Curlee

27. My son always tells the truth ^ v ~ My Father is a liar p q Quiz Determine if the proposition is simple or compound and Symbolized the propositions. 1 If I lose then I quit Ramon is a great singer but their family is poor Sander likes chocolate while Sandreah prefers Vanilla Either Romuldes is Guilty or he is Innocent Buy one take one You are Pretty Kiko is a Good Public Servant Tito Sotto is an Independent Politician who only serve the people Duterte is Innocent You are my everything Negate the Following Propositions

28. My son always tells the truth ^ v ~ My Father is a liar p q Learning Competency: Illustrate Different forms of Conditional Proposition A 1 B Illustrate Converse, Inverse and Contrapositive Define a Counter Example Objectives: B

29. My son always tells the truth ^ v ~ My Father is a liar p q Activity/Drill P implies Q Give the Symbolical Form of the Propositions and it Truth Value 1 Q implies P Not P implies not Q Not Q implies not P P implies Q and Q implies P

30. My son always tells the truth ^ v ~ My Father is a liar p q Counter Example A Counter Example of a Conditional statements is an argumentative Example that negates the conclusion of a Conditional Statement with a Assumed True Hypothesis . Thus making the entire statement false. 1 If you love me then you will respect me In the Conditional statement the proposition “ you love me ” the hypothesis is assumed true. To determine weather the statement is true we need to ascertain the truthfulness of the proposition “ you will respect me ”

31. My son always tells the truth ^ v ~ My Father is a liar p q Counter Example 1 If you love me then you will respect me In the Conditional statement the proposition “ you love me ” the hypothesis is assumed true. To determine weather the statement is true we need to ascertain the truthfulness of the proposition “ you will respect me ”. The consequent of the Argument will result to a final Conclusion. You do not love me because you are not respecting me

32. My son always tells the truth ^ v ~ p q Activity # 1 If you believe in GOD then follow his Commandments. If you want to be successful someday then Study diligently. If it is a polygon with 4 sided then it is a Parallelogram. Disprove the following statement. Provide a Logical Counter Example for the following Conditional Statement If a number is divisible by 3 then it is divisible by 9. If you want to be save then you need to be in our religion.

33. My son always tells the truth ^ v ~ My Father is a liar p q Inverse of a Conditional Statement 1 Conditional If you love me then you will respect me When a Conditional Statement was disprove its Inverse will be True. The Inverse of a Conditional is the Negation of P that Implies a negation of. Inverse of a Conditional If you do not love me then you are not respecting me You do not love me because you are not respecting me

34. My son always tells the truth ^ v ~ My Father is a liar p q Inverse of a Conditional Determine the Inverses of the Following Statements 1 If you love me then you will respect me. If you want to be successful someday then Study diligently. If it is a polygon with 4 sided then it is a Parallelogram. If a number is divisible by 3 then it is divisible by 9. If you want to be save then you need to be in our religion.

35. My son always tells the truth ^ v ~ My Father is a liar p q Fallacy of affirming the Consequent 1 Conditional If you believe in GOD then follow his Commandments. When a Conditional Statement has a tendency of affirming a fallacy of Consequent by introducing its Converse. The Converse of a Conditional Statement is Formed by swapping the Conclusion to the Hypothesis. Converse of a Conditional If follow his Commandments then you believe in GOD You follow his Commandment because you believe in GOD

36. My son always tells the truth ^ v ~ My Father is a liar p q Converse of a Conditional Determine the Converse of the Following Statements 1 If you believe in GOD then follow his Commandments. If you want to be successful someday then Study diligently. If it is a polygon with 4 sided then it is a Parallelogram. If a number is divisible by 3 then it is divisible by 9. If you want to be save then you need to be in our religion.

37. My son always tells the truth ^ v ~ My Father is a liar p q The Equivalent of Conditional 1 Conditional If you believe in GOD then follow his Commandments. Conditional Statement has its Equivalent statement called the Contrapositive. It is formed by negating a Q implying a negated P Contrapositive of a Conditional If will not follow his Commandments then you do not believe in GOD You do not follow his Commandment because you did not believe in GOD

38. My son always tells the truth ^ v ~ My Father is a liar p q Contrapositive of a Conditional Determine the Contrapositive of the Following Statements 1 If you love me then you will respect me. If you want to be successful someday then Study diligently. If it is a polygon with 4 sided then it is a Parallelogram. If a number is divisible by 3 then it is divisible by 9. If you want to be save then you need to be in our religion.

39. My son always tells the truth ^ v ~ My Father is a liar p q Symbolism in Proposition Propositions are symbolized using a first letter of the main thought of the proposition. 1 It is a Cloudy Today the proposition can be Symbolized as “ C ” Monkey Eats Banana the proposition can be Symbolized as “ M ”or “ B ”

40. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 CONJUNCTION simple propositions connected using the word “ and ” and symbolized as “ ^ ” R: Roses are Red S: The Sky is Blue Roses are Red and the Sky is Blue “R ^ S”

41. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 CONJUNCTION “ but ” can also use instead of and if the propositions are opposite in nature. R: I love you S: I lie I Love you but I lie “U ^ L”

42. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 DISJUNCTION are simple propositions that are connected using the word “ or ” and symbolled as “ v ” . M: He watches a movie D: He dines with his friends (Either) he watches a movie or dines with his friends “M v D”

43. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 S: I Study well E: I will pass the Exam If I study well then I will pass the exam Conditional are simple propositions that are connected using the word “ if ” …..“ then ” it is represented as p q “S D”

44. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 Conditional are simple propositions that are connected using the word “ if ” …..“ then ” it is represented as p q S: I Study well E: I will pass the Exam If I study well then I will pass the exam “S D”

45. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 Antecedent and Consequent The Antecedent (Hypothesis) is the ‘’ P ” statement and Consequent (Conclusion) is the “ Q ” in the p q If I study well then I will pass the exam Antecedent Conclusion

46. My son always tells the truth ^ v ~ My Father is a liar p q Compound Propositions Are Statement compose of several proposition combined by connectives 1 NEGATION The negation of a given statement is a statement that is flase whanever the given statement is true and true whenever the given statement is false “ ~ ” P : I will pass the Exam ~P : I will not pass the exam / I will fail the Exam

47. My son always tells the truth ^ v ~ My Father is a liar p q Activity Determine if it simple or compound Proposition 1 Bamboo are Grass I win or I Lose I work efficiently but it makes me tired If it rains then the road is wet Sarah loves Curlee

48. My son always tells the truth ^ v ~ My Father is a liar p q Activity Symbolized the following Propositions 1 Bamboo are Grass I win or I Lose I work efficiently but it makes me tired If it rains then the road is wet Sarah loves Curlee

49. My son always tells the truth ^ v ~ My Father is a liar p q Quiz Determine if the proposition is simple or compound and Symbolized the propositions. 1 If I lose then I quit Ramon is a great singer but their family is poor Sander likes chocolate while Sandreah prefers Vanilla Either Romuldes is Guilty or he is Innocent Buy one take one You are Pretty Kiko is a Good Public Servant Tito Sotto is an Independent Politician who only serve the people Duterte is Innocent You are my everything Negate the Following Propositions