1. Problem of Day Problem of Day Return Test and Show Magazine/Newspaper Honors Try These 3 Problems Regular Try These 2 Problems 1. C 2. x = 50 3. D 1. D 2. C

2. Section 1 “Conditional Statements” #1

3. Conditional Statements “if, then Statements” If an angle is straight, then it is 180. If Hypothesis, then Conclusion (P  Q) Symbol: if p, then q (P  Q)

4. Example #1 Write the Hypothesis p and Conclusion q I. If you live in Suffolk, then you live in Virginia. II. If an angle is less than 90 Degrees, then it is acute. I. p  You live in Suffolk q  You live in Virginia II. p  An angle is less than 90 Degrees q  It is acute

5. Ex #I and II. Write each as a Conditional Sentence I. If a figure is a rectangle, then it has four right angles. II. If two lines intersect at a right angle, then those two lines are perpendicular.

6. Converse Statements (Flip Conditional) Conditional: If p, then q Converse: If q, then p Symbol:p  q q  pq  p

7. Ex #III and IV. Write the Conditional as a Converse I. If lines do not intersect, then they are parallel lines. II. If the measure of an angle is 90, then it is Complementary.

8. (~) Conditional Statements w/Negations (~) Negation Negation—Means not (or opposite)

9. Inverse Inverse: Inverse:If not p, then not q Symbol:~p  ~q Ex #V. and VI.:Write each as an Inverse Statement does not not I. If an angle does not measure 90 degrees, then it is not a right angle. do not do not II. If you do not live in North Carolina, then you do not live in the US.

10. Contrapositive (Flip Inverse) Inverse:If ~p, then ~q Contrapositive:~q  ~p

11. Ex #VII and VIII.: Write the Contrapositive of Each (If ~q, then ~p): I. If two lines are not equal, then they are not congruent. II. If the angle is not obtuse, then <LMN does not equal 112 degrees.

12. Example #2 Write the Converse, Inverse, and Contrapositive Statements from the Conditional Statement? “If angle m<BOC is 35, then angle <BOC is acute.” Converse: Inverse: Contrapositive:

13. Key Symbols (Look at the Sheet) Conditional:if p then q Converse:if q then p Inverse:if ~p then ~q Contrapositive:if ~q then ~p v:OR ^:AND Three Dots:Therefore

14. Biconditional When a Conditional and Converse are true, you combine them as a Biconditional. if and only if These phrases are joined as if and only if. p if and only if q pq p  q

15. Example #3: Write the Biconditional Statement If three points are collinear, then they lie on the same line. If three points lie on the same line, then the points are collinear. Three points are collinear if and only if they are on the same line.

16. Example #4 Let m represent: Angle A is obtuse. Let n represent: Angle B is obtuse. Which is a symbolic representation of the following argument? Angle A is obtuse if and only if Angle B is obtuse. Angle A is obtuse or Angle B is obtuse. Therefore, Angle A is obtuse and Angle B is obtuse. A.m → nB. m → nC. m ↔ n D. m ↔ n m ∧ n m ∨ n ∴ m ∨ n ∴ m ∧ n 16

17. Example #5 Let p represent: The sum of two angles is 180. Let q represent: The two angles are Supplements. Which is a symbolic representation of the following argument? “Two Angles are not Supplements if and only if the sum of the two angle is not 180.” A. ~q  ~p B. ~p  ~q C. q  p D. p  q 17

18. Exit Slip “Conditional Statements” (+11pts) 1. Worksheet—Conditional Statements 2. Conditional Statements Advertisement Project Worth: +22 Points (Quiz Grade) 1 st, 3 rd, and 5 th Blocks [Due: By Friday, October 24 th ] 2 nd and 4 th Blocks [Due: By Next Monday, October 27 th ]

19. Problem of the Day **Check Homework, Project Due Next Class** Try these Four Problems: 1. Write the Converse, Inverse, Contrapositive Statements of: “If <BOC is 100 degrees, then <BOC is obtuse.” Converse: Inverse: Contrapositive: 2. A. 3. B. 4. B.

20. Laws of Syllogism and Detachment

21. Law of Syllogism “Two conditional statements making one statement from the 1 st Hypothesis and 2 nd Conclusion.” Symbol: p  r p  q and q  r, then q’s cancel to make p  r.

22. Ex #1: Use the Law of Syllogism If a number is prime, then it does not have repeated figures. If a number does not have repeated figures, then it is not a perfect square. By Law of Syllogism, p  q and q  r, then p  r If a number is prime, then it is not a perfect square.

23. Ex #2: Use the Law of Syllogism If a quadrilateral is a rhombus, then it is a parallelogram. If a quadrilateral is a parallelogram, then its opposite angles are congruent. By Law of Syllogism, p  q and q  r, then p  r If a quadrilateral is a rhombus, then its opposite angles are congruent.

24. Ex #3: Use the Law of Syllogism Some Musicians are happy people. All happy people like music. By Law of Syllogism, p  q and q  r, then p  r Some Musicians like Music.

25. Law of Detachment “A Conditional Statement and a matched second statement p, to make a new conclusion q.” (answer is q) p  q and a same p to make a new q (answer is q)

26. Ex #4: Use the Law of Detachment If m<ABC is acute, then the angle is less than 90 Degrees. m<ABC is acute. By Law of Detachment: (answer involves q): p  q and a same p, thus a new q (answer involves q): m<ABC is less than 90 Degrees.

27. Ex #5: Use the Law of Detachment If x = 3, then 3x – 4 = 5. If x = 3. By Law of Detachment: (answer involves q): p  q and a same p, thus a new q (answer involves q): 3x – 4 = 5

28. Both Laws Both Laws (3 Statements) 1. Use Syllogism with first two statements. Then, use Detachment to make final answer with the third, r, statement. 2. Answer is new r.

29. Ex #6: Use Both Laws 1. If you live in Little Rock, then you live in Arkansas. 2. If you live in Arkansas, then you live in the 25 th state to enter the United States. 3. Bob lives in Little Rock. Law of Syllogism: “If you live in Little Rock, then you live in the 25 th state to enter the United States.” Law of Detachment: Bob lives in the 25 th state to enter the United States.

30. Ex #7: Use Both Laws 1. If the circus is in town, then there are tents at the fairgrounds. 2. If there are tents at the fairgrounds, then Naya is working as a night watchperson. 3. The circus is in town. Law of Syllogism: “If the circus is in town, then Naya is working as a night watchman.” Law of Detachment: Naya is working as a night watchperson.

31. 1. Exit Slip (+8 pts) 2. Laws Worksheet 3. Conditional Statements Advertisement Project Worth: +22 Points (Quiz Grade) Due Next Class Block

32. Problems of the Day (Review of last 2 Classes) Problems of the Day (Review of last 2 Classes) Check Homework + Collect Project [+8pts—Grade and Tell Points] 8. Let p: x^2 = 21 Let q: x is not a whole number. What is the p and q representation of the statement below? If x is a whole number, then x^2 = 21 1. B 2. A 3. B 4. A 5. C 6. A 7. B 8. ~q  p

33. 1. Venn Diagrams w/Activity 2. Truth Tables (Honors)

34. Example #1— Write the Conditional (p  q) Statement Illustrated by each Venn Diagram? I. All Pitchers are Baseball Players II. Integers divisible by 4 are always divisible by 2. Baseball Players Pitchers 2 4

35. Try Examples #2, 3, and 4 Example #2 Example #3 I. B II. C III. A Example #4 B. Section II I. 16 II. 19 III. 41 IV. 5 V. 7

36. Example #5: Make Venn Diagrams for each I. Some Ice Cream is Vanilla. II. All Skiers have skis or boots.

37. Worth: +36 pts Create a Venn Diagram for each by cutting out each of the Circles and Conditional Statements

38. 1. Venn Diagram Homework 2. If not done, Advertisement Project 3. Next Thursday or this Friday is Final Exam Test 4. End of Quarter is Monday, November 3 rd [All Missing Work is due that day]

39. Truth Tables w/Two Rules Tables that list all possible combinations of truth values of Compound Combined Statements. Answers are either T True or F False. 1. Any True with OR makes True 2. Any Double True with AND makes True

40. Compound Statements 2 TypesSymbol Conjunction AND ^ Disjunction OR

41. To Construct Truth Tables 1. Set up of P and Q Truth Tables? PQ TT TF FT FF

42. Example #I. Make p ^ q Truth Table PQP ^Q TTT TFF FTF FFF

43. Example #II. Make p V q Truth Table PQP V Q TTT TFT FTT FFF

44. Example #III. Make ~p V q Truth Table PQ~PP V Q TTFT TFFF FTTT FFTT

45. Example #IV. Make ~p ^ q Truth Table PQ~PP ^ Q TTFF TFFF FTTT FFTF

46. 1. Venn Diagram and Truth Table Homework 2. If not done, Advertisement Project 3. Next Thursday is Final Exam Test 4. End of Quarter is Monday, November 3 rd [All Missing Work is due that day]

47. Problem of Day Problem of Day **Collect Venn Diagram Activity, Show Worksheet, and Final Exam Next Class** ##End of Quarter and Late Work is Due Next Monday, Nov. 3 rd ## Honors Try These 4 Problems Regular Try These 5 Problems 1. Truth Table 2. C. -5 3. A. 10 4. D. 112 1. x = 46 2. x = 43 3. C. -7/8 4. C. -5 5. X = 4 and m<1 = 26 PQP ^Q TTT TFF FTF FFF

48. Remember plus 1 Problem Consecutive Angles + = 180 while everything else is =. Let a: “x is an even number” Let b: “x is a multiple of 4” When x is 30, which of the following is True? I. a ^ b II. a ^ ~b III. ~a ^ ~b IV. ~a ^ b

49. 1. STUDY FOR FINAL EXAM 2. If not done, Project 3. End of Quarter Monday + Late Work due Monday

50. 1. Word Search Extra Credit 2. SOL Homework #3 (+15pts) 3. UNIT 3 Logic TEST --1, 3 and 5 th Blocks [Next Thursday, November 6th] --2 and 4 th Blocks[Next Friday, November 7th]

51. 24. C #14 and #18 are the Same Problem

52. 22. C

53. I. Find the coordinates of a point lying on a line which passes thru point P and is parallel to line c. II. Find the coordinates of a point lying on a line which passes thru point P and is perpendicular to line c. Problem of the Day **Collect SOL Homework #3, Test Next Class** #4) The Coordinates are (-1, 2) and (5, -2) P c

54. 1. DI Carousel Activity (+20pts) Exploring Angle Pairs 2. Logic Unit 3 Review (+30 pts) 3. Questions before the Unit 3 Logic Test Next Class

55. Problem #11: Make Venn Diagrams for each I. Some Cars are Fords. II. All Students take Gym or Art. III. No Freshmen take Calculus. IV. If you plant an oak, then you planted a Tree.

56. Problem of the Day **Then Test, Then Easy Notes** 1) Put Words into each Circle For #2-3, Multiple Choice: 2) F 3) D

57. Extra Credit + New Notes

58. #22 and #23 (Honors) Make Two Tables #22. P ^ Q #23. P v Q