1. Geometry Pre-AP
BOMLA LacyMath
10/6

3. “My logic is undeniable!”
Logic (Chapter 2-2)

4. Making a Statement
A statement is any sentence that is true or false.

5. Making a Statement A statement is any sentence that is true or false.
DUH!!!! Right????

6. Making a Statement A statement is any sentence that is true or false.
DUH!!!! Right????
They can either be true or false, but not both. Whether a statement is true or false is called its truth value (sometimes called the “validity” of the statement).
Statements are often represented using a letter such as p or q.

7. Making a Statement
True or False???
p: BOMLA is an all boys school.

8. Making a Statement True or False??? p: BOMLA is an all boys school.
p is true!

9. Making a Statement
True or False???
q: Mr. Lacy is 28 years old.

10. Making a Statement True or False??? q: Mr. Lacy is 28 years old.
q is false!!! (as of September 26)

11. Making a Statement True or False???
p: Our school has now been open for 6 years.

12. Making a Statement True or False???
p: Our school has now been open for 6 years.
p is true!!!

13. Making a Statement True or False???
q: You can name a plane using a capital script letter and 4 non-collinear points.

14. Making a Statement True or False???
q: You can name a plane using a capital script letter and 4 non-collinear points.
q is false!!! (It’s 3 non-collinear points.)

15. “On the contrary…”
The negation of a statement has the opposite meaning as well as an opposite truth value.
~ p which is read “not p”
~ q which is read “not q”

16. Making a Statement p: BOMLA is an all boys school. p is true!
~ p: BOMLA is not an all boys school.

17. Making a Statement p: BOMLA is an all boys school. p is true!
~ p: BOMLA is not an all boys school.
~ p is false!

18. Making a Statement
q: You can name a plane using a capital script letter and 4 non-collinear points.
q is false!!! (It’s 3 non-collinear points.)
~ q : You can not name a plane using a capital script letter and 4 non-collinear points.

19. Making a Statement
q: You can name a plane using a capital script letter and 4 non-collinear points.
q is false!!! (It’s 3 non-collinear points.)
~ q : You can not name a plane using a capital script letter and 4 non-collinear points.
~ q is true!!!

20. Putting Statements Together
Compound statement – when two or more statements are joined together. They can be joined by the word “or” or the word “and”.

21. Putting Statements Together
Conjunction – joining two or more statements with “and”
Conjunctions are only true when BOTH statements are true.
Use the symbol ∧ between letters.

22. Putting Statements Together
Conjunction – joining two or more statements with “and”
Example 1
p: The number 2 is even.
q: The number 2 is prime.

23. Putting Statements Together
Conjunction – joining two or more statements with “and”
Example 1
p: The number 2 is even.
q: The number 2 is prime.
The number 2 is even, AND the number 2 is prime.

24. Putting Statements Together
Conjunction – joining two or more statements with “and”
Example 1
p: The number 2 is even.
q: The number 2 is prime.
The number 2 is even, AND the number 2 is prime.
p ∧ q is TRUE!!!

25. Putting Statements Together
Conjunction – joining two or more statements with “and”
Example 2
p: The number 3 is even.
q: The number 2 is prime.

26. Putting Statements Together
Conjunction – joining two or more statements with “and”
Example 2
p: The number 3 is even.
q: The number 2 is prime.
The number 3 is even, AND the number 2 is prime.

27. Putting Statements Together
Conjunction – joining two or more statements with “and”
Example 2
p: The number 3 is even.
q: The number 2 is prime.
The number 3 is even, AND the number 2 is prime.
p ∧ q is FALSE!!!

28. Putting Statements Together
Disjunction – joining two or more statements with “or”
Disjunctions are true when AT LEAST ONE statement is true.
Use the symbol v between letters.

29. Putting Statements Together
Disjunction – joining two or more statements with “or”
Back to Example 2
p: The number 3 is even.
q: The number 2 is prime.

30. Putting Statements Together
Disjunction – joining two or more statements with “or”
Back to Example 2
p: The number 3 is even.
q: The number 2 is prime.
The number 3 is even, OR the number 2 is prime.

31. Putting Statements Together
Disjunction – joining two or more statements with “or”
Back to Example 2
p: The number 3 is even.
q: The number 2 is prime.
The number 3 is even, OR the number 2 is prime.
p v q is TRUE!!!

32. Putting Statements Together
Disjunction – joining two or more statements with “or”
Example 3
p: Dogs only have 2 legs.
q: Cats lay eggs.

33. Putting Statements Together
Disjunction – joining two or more statements with “or”
Example 3
p: Dogs only have 2 legs.
q: Cats lay eggs.
Dogs only have 2 legs, OR cats lay eggs.

34. Putting Statements Together
Disjunction – joining two or more statements with “or”
Example 3
p: Dogs only have 2 legs.
q: Cats lay eggs.
Dogs only have 2 legs, OR cats lay eggs.
p v q is FALSE!!!

35. Determine truth value of the Statements
Compound Statement
Determine truth value of the Statements
Conjunction
Both True? T F
Disjunction
At Least 1 True?

36. Compound Statements Example 4
p: Mr. Douglas’ first name starts with an “N”.
q: The school day at BOMLA begins at 7am.
Mr. Douglas’ first name starts with an “N”, and the school day at BOMLA begins at 7am.
p ∧ q is
Mr. Douglas’ first name starts with an “N”, or the school day at BOMLA begins at 7am.
p v q is

37. Compound Statements Example 4
p: Mr. Douglas’ first name starts with an “N”.
q: The school day at BOMLA begins at 7am.
Mr. Douglas’ first name starts with an “N”, and the school day at BOMLA begins at 7am.
p ∧ q is FALSE
Mr. Douglas’ first name starts with an “N”, or the school day at BOMLA begins at 7am.
p v q is

38. Compound Statements Example 4
p: Mr. Douglas’ first name starts with an “N”.
q: The school day at BOMLA begins at 7am.
Mr. Douglas’ first name starts with an “N”, and the school day at BOMLA begins at 7am.
p ∧ q is FALSE
Mr. Douglas’ first name starts with an “N”, or the school day at BOMLA begins at 7am.
p v q is TRUE

39. Compound Statements Example 5 p: 9 + 5 = 14 q: February has 30 days.
r: A square has four sides.
9 + 5 = 14, and February has 30 days.
9 + 5 = 14, or February has 30 days.

40. Compound Statements Example 5 p: 9 + 5 = 14 q: February has 30 days.
r: A square has four sides.
9 + 5 = 14, and February has 30 days.
p ∧ q is
9 + 5 = 14, or February has 30 days.
p v q is

41. Compound Statements Example 5 p: 9 + 5 = 14 q: February has 30 days.
r: A square has four sides.
9 + 5 = 14, and February has 30 days.
p ∧ q is FALSE!!!
9 + 5 = 14, or February has 30 days.
p v q is

42. Compound Statements Example 5 p: 9 + 5 = 14 q: February has 30 days.
r: A square has four sides.
9 + 5 = 14, and February has 30 days.
p ∧ q is FALSE!!!
9 + 5 = 14, or February has 30 days.
p v q is TRUE!!!

43. Compound Statements Example 5 p: 9 + 5 = 14 q: February has 30 days.
r: A square has four sides.
9 + 5 = 14, and a square has four sides.
p ∧ r is
9 + 5 = 14, or a square has four sides.
p v r is

44. Compound Statements Example 5 p: 9 + 5 = 14 q: February has 30 days.
r: A square has four sides.
9 + 5 = 14, and a square has four sides.
p ∧ r is TRUE!!!
9 + 5 = 14, or a square has four sides.
p v r is

45. Compound Statements Example 5 p: 9 + 5 = 14 q: February has 30 days.
r: A square has four sides.
9 + 5 = 14, and a square has four sides.
p ∧ r is TRUE!!!
9 + 5 = 14, or a square has four sides.
p v r is TRUE!!!

46. Compound Statements Example 5 p: 9 + 5 = 14 q: February has 30 days.
r: A square has four sides.
~ p ∧ r is
p ∧ ~ q is

47. Compound Statements Example 5 p: 9 + 5 = 14 q: February has 30 days.
r: A square has four sides.
~ p ∧ r is FALSE!!!
p ∧ ~ q is

48. Compound Statements Example 5 p: 9 + 5 = 14 q: February has 30 days.
r: A square has four sides.
~ p ∧ r is FALSE!!!
p ∧ ~ q is TRUE!!!

49. Another Way to Look At Things…
Conjunctions and Disjunctions can also be displayed using Venn diagrams.

50. Another Way to Look At Things…
Conjunctions and Disjunctions can also be displayed using Venn diagrams.

51. Another Way to Look At Things…
Conjunctions and Disjunctions can also be displayed using Venn diagrams.
Which section represents ____ ∧ ____ ?

52. Another Way to Look At Things…
Conjunctions and Disjunctions can also be displayed using Venn diagrams.
Which section represents ____ ∧ ____ ?
Which section represents ____ v ______ ?

53. Another Way to Look At Things…
A truth table is a method for organizing truth values of statements. They can be used to determine the truth values of negations and compound statements.

54. Another Way to Look At Things…
Truth Table
Negation p
~ p T F

55. Another Way to Look At Things…
Truth Table
Negation p
~ p T F

56. Another Way to Look At Things…
Truth Table
Negation p
~ p T F

57. Another Way to Look At Things…
Truth Table
Conjunction p q
p ∧ q T F

58. Another Way to Look At Things…
Truth Table
Conjunction p q
p ∧ q T F

59. Another Way to Look At Things…
Truth Table
Conjunction p q
p ∧ q T F

60. Another Way to Look At Things…
Truth Table
Conjunction p q
p ∧ q T F

61. Another Way to Look At Things…
Truth Table
Conjunction p q
p ∧ q T F

62. Another Way to Look At Things…
Truth Table
Disjunction p q
p v q T F

63. Another Way to Look At Things…
Truth Table
Disjunction p q
p v q T F

64. Another Way to Look At Things…
Truth Table
Disjunction p q
p v q T F

65. Another Way to Look At Things…
Truth Table
Disjunction p q
p v q T F

66. Another Way to Look At Things…
Truth Table
Disjunction p q
p v q T F

67. CW 02 – My Logic is Undeniable Pg. 103 #11-16, 18, 20, 22 Pg. 104
Classwork
CW 02 – My Logic is Undeniable
Pg. 103
#11-16, 18, 20, 22
Pg. 104
#23, 31
First 7 minutes individual