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# Geometry Section 2-2 1112

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### Transcript of "Geometry Section 2-2 1112"

1. 1. SECTION 2-2 Logic Thursday, November 6, 14
2. 2. Essential Questions How do you determine truth values of negatives, conjunctions, disjunctions, and represent them using Venn diagrams? Thursday, November 6, 14
3. 3. Vocabulary 1. Statement: 2. Truth Value: 3. Negation: 4. Compound Statement: 5. Conjunction: 6. Disjunction: 7. Truth Table: Thursday, November 6, 14
4. 4. Vocabulary 1. S t a t e m e n t : A sentence that is either true or false, often represented as statements p and q 2. Truth Value: 3. Negation: 4. Compound Statement: 5. Conjunction: 6. Disjunction: 7. Truth Table: Thursday, November 6, 14
5. 5. Vocabulary 1. S t a t e m e n t : A sentence that is either true or false, often represented as statements p and q 2. Truth Value: The statement is either true (T) or false (F) 3. Negation: 4. Compound Statement: 5. Conjunction: 6. Disjunction: 7. Truth Table: Thursday, November 6, 14
6. 6. Vocabulary 1. S t a t e m e n t : A sentence that is either true or false, often represented as statements p and q 2. Truth Value: The statement is either true (T) or false (F) 3. N e g a t i o n : A statement with the opposite meaning and opposite truth value; the negation of p is ~p 4. Compound Statement: 5. Conjunction: 6. Disjunction: 7. Truth Table: Thursday, November 6, 14
7. 7. Vocabulary 1. S t a t e m e n t : A sentence that is either true or false, often represented as statements p and q 2. Truth Value: The statement is either true (T) or false (F) 3. N e g a t i o n : A statement with the opposite meaning and opposite truth value; the negation of p is ~p 4. C o m p o u n d S t a t e m e n t : Two or more statements joined by and or or 5. Conjunction: 6. Disjunction: 7. Truth Table: Thursday, November 6, 14
8. 8. Vocabulary 1. S t a t e m e n t : A sentence that is either true or false, often represented as statements p and q 2. Truth Value: The statement is either true (T) or false (F) 3. N e g a t i o n : A statement with the opposite meaning and opposite truth value; the negation of p is ~p 4. C o m p o u n d S t a t e m e n t : Two or more statements joined by and or or 5. Conjunction: 6. Disjunction: 7. Truth Table: A compound statement using the word and or symbol ∧ Thursday, November 6, 14
9. 9. Vocabulary 1. S t a t e m e n t : A sentence that is either true or false, often represented as statements p and q 2. Truth Value: The statement is either true (T) or false (F) 3. N e g a t i o n : A statement with the opposite meaning and opposite truth value; the negation of p is ~p 4. C o m p o u n d S t a t e m e n t : Two or more statements joined by and or or 5. Conjunction: 6. Disjunction: 7. Truth Table: A compound statement using the word and or symbol ∧ A compound statement using the word or or symbol ∨ Thursday, November 6, 14
10. 10. Vocabulary 1. S t a t e m e n t : A sentence that is either true or false, often represented as statements p and q 2. Truth Value: The statement is either true (T) or false (F) 3. N e g a t i o n : A statement with the opposite meaning and opposite truth value; the negation of p is ~p 4. C o m p o u n d S t a t e m e n t : Two or more statements joined by and or or 5. Conjunction: 6. Disjunction: 7. Truth Table: A way to organize truth values of statements A compound statement using the word and or symbol ∧ A compound statement using the word or or symbol ∨ Thursday, November 6, 14
11. 11. Example 1 Use the following statements to write a compound sentence for each conjunction. Then find its truth value. Explain your reasoning. p: One meter is 100 mm q: November has 30 days r: A line is defined by two points a. p and q b. ~ p ∧ r Thursday, November 6, 14
12. 12. Example 1 Use the following statements to write a compound sentence for each conjunction. Then find its truth value. Explain your reasoning. p: One meter is 100 mm q: November has 30 days r: A line is defined by two points a. p and q One meter is 100 mm and November has 30 days b. ~ p ∧ r Thursday, November 6, 14
13. 13. Example 1 Use the following statements to write a compound sentence for each conjunction. Then find its truth value. Explain your reasoning. p: One meter is 100 mm q: November has 30 days r: A line is defined by two points a. p and q One meter is 100 mm and November has 30 days q is true, but p is false, so the conjunction is false b. ~ p ∧ r Thursday, November 6, 14
14. 14. Example 1 Use the following statements to write a compound sentence for each conjunction. Then find its truth value. Explain your reasoning. p: One meter is 100 mm q: November has 30 days r: A line is defined by two points a. p and q One meter is 100 mm and November has 30 days q is true, but p is false, so the conjunction is false b. ~ p ∧ r One meter is not 100 mm and a line is defined by two points Thursday, November 6, 14
15. 15. Example 1 Use the following statements to write a compound sentence for each conjunction. Then find its truth value. Explain your reasoning. p: One meter is 100 mm q: November has 30 days r: A line is defined by two points a. p and q One meter is 100 mm and November has 30 days q is true, but p is false, so the conjunction is false b. ~ p ∧ r One meter is not 100 mm and a line is defined by two points Both ~p and r are true, so is true ~ p ∧ r Thursday, November 6, 14
16. 16. Example 2 Use the following statements to write a compound statement for each disjunction. Then find its truth value. Explain your reasoning. q: Kilometers are metric units p: AB is proper notation for “ray AB” r: 15 is a prime number a. p or q b. q ∨ r Thursday, November 6, 14
17. 17. Example 2 Use the following statements to write a compound statement for each disjunction. Then find its truth value. Explain your reasoning. q: Kilometers are metric units p: AB is proper notation for “ray AB” r: 15 is a prime number a. p or q AB is proper notation for “ray AB” or kilometers are metric units b. q ∨ r Thursday, November 6, 14
18. 18. Example 2 Use the following statements to write a compound statement for each disjunction. Then find its truth value. Explain your reasoning. q: Kilometers are metric units p: AB is proper notation for “ray AB” r: 15 is a prime number a. p or q AB is proper notation for “ray AB” or kilometers are metric units Both p and q are true, so p or q is true b. q ∨ r Thursday, November 6, 14
19. 19. Example 2 Use the following statements to write a compound statement for each disjunction. Then find its truth value. Explain your reasoning. q: Kilometers are metric units p: AB is proper notation for “ray AB” r: 15 is a prime number a. p or q AB is proper notation for “ray AB” or kilometers are metric units Both p and q are true, so p or q is true b. q ∨ r Kilometers are metric units or 15 is a prime number Thursday, November 6, 14
20. 20. Example 2 Use the following statements to write a compound statement for each disjunction. Then find its truth value. Explain your reasoning. q: Kilometers are metric units p: AB is proper notation for “ray AB” r: 15 is a prime number a. p or q AB is proper notation for “ray AB” or kilometers are metric units Both p and q are true, so p or q is true b. q ∨ r Kilometers are metric units or 15 is a prime number Since one of the statements (q) is true, is true q ∨ r Thursday, November 6, 14
21. 21. Example 2 Use the following statements to write a compound statement for each disjunction. Then find its truth value. Explain your reasoning. q: Kilometers are metric units p: AB is proper notation for “ray AB” r: 15 is a prime number c. ~ p ∨ r Thursday, November 6, 14
22. 22. Example 2 Use the following statements to write a compound statement for each disjunction. Then find its truth value. Explain your reasoning. q: Kilometers are metric units p: AB is proper notation for “ray AB” r: 15 is a prime number c. ~ p ∨ r AB is not proper notation of “ray AB” or 15 is a prime number Thursday, November 6, 14
23. 23. Example 2 Use the following statements to write a compound statement for each disjunction. Then find its truth value. Explain your reasoning. q: Kilometers are metric units p: AB is proper notation for “ray AB” r: 15 is a prime number c. ~ p ∨ r AB is not proper notation of “ray AB” or 15 is a prime number Since both ~p and r are false, is false ~ p ∨ r Thursday, November 6, 14
24. 24. Example 3 Construct a truth table for the following. a. p ∧ q Thursday, November 6, 14
25. 25. Example 3 Construct a truth table for the following. a. p ∧ q p q p ∧ q T T T T F F F T F F F F Thursday, November 6, 14
26. 26. Example 3 Construct a truth table for the following. a. p ∧ q p q p ∧ q T T T T F F F T F F F F Thursday, November 6, 14
27. 27. Example 3 Construct a truth table for the following. a. p ∧ q p q p ∧ q T T T T F F F T F F F F Thursday, November 6, 14
28. 28. Example 3 Construct a truth table for the following. b. ~ p ∧ (~ p ∨ q ) Thursday, November 6, 14
29. 29. Example 3 Construct a truth table for the following. b. ~ p ∧ (~ p ∨ q ) p q ~p ~p∨q ~p∧(~p∨q) T T F T F T F F F F F T T T T F F T T T Thursday, November 6, 14
30. 30. Example 3 Construct a truth table for the following. b. ~ p ∧ (~ p ∨ q ) p q ~p ~p∨q ~p∧(~p∨q) T T F T F T F F F F F T T T T F F T T T Thursday, November 6, 14
31. 31. Example 3 Construct a truth table for the following. b. ~ p ∧ (~ p ∨ q ) p q ~p ~p∨q ~p∧(~p∨q) T T F T F T F F F F F T T T T F F T T T Thursday, November 6, 14
32. 32. Example 3 Construct a truth table for the following. b. ~ p ∧ (~ p ∨ q ) p q ~p ~p∨q ~p∧(~p∨q) T T F T F T F F F F F T T T T F F T T T Thursday, November 6, 14
33. 33. Example 3 Construct a truth table for the following. b. ~ p ∧ (~ p ∨ q ) p q ~p ~p∨q ~p∧(~p∨q) T T F T F T F F F F F T T T T F F T T T Thursday, November 6, 14
34. 34. Example 4 The Venn diagram shows the number of students enrolled in Maggie Brann’s Dance School for tap, jazz, and ballet classes. Tap 28 Jazz 43 Ballet 29 17 25 9 25 a. How many students are enrolled in all three classes? b. How many students are enrolled in tap or ballet? c. How many students are enrolled in jazz and ballet, but not tap? Thursday, November 6, 14
35. 35. Example 4 The Venn diagram shows the number of students enrolled in Maggie Brann’s Dance School for tap, jazz, and ballet classes. Tap 28 Jazz 43 Ballet 29 17 25 9 25 a. How many students are enrolled in all three classes? 9 students b. How many students are enrolled in tap or ballet? c. How many students are enrolled in jazz and ballet, but not tap? Thursday, November 6, 14
36. 36. Example 4 The Venn diagram shows the number of students enrolled in Maggie Brann’s Dance School for tap, jazz, and ballet classes. Tap 28 Jazz 43 Ballet 29 17 25 9 25 a. How many students are enrolled in all three classes? 9 students b. How many students are enrolled in tap or ballet? 28 + 25 + 9 + 17 + 29 +25 c. How many students are enrolled in jazz and ballet, but not tap? Thursday, November 6, 14
37. 37. Example 4 The Venn diagram shows the number of students enrolled in Maggie Brann’s Dance School for tap, jazz, and ballet classes. Tap 28 Jazz 43 Ballet 29 17 25 9 25 a. How many students are enrolled in all three classes? 9 students b. How many students are enrolled in tap or ballet? 28 + 25 + 9 + 17 + 29 +25 133 students c. How many students are enrolled in jazz and ballet, but not tap? Thursday, November 6, 14
38. 38. Example 4 The Venn diagram shows the number of students enrolled in Maggie Brann’s Dance School for tap, jazz, and ballet classes. Tap 28 Jazz 43 Ballet 29 17 25 9 25 a. How many students are enrolled in all three classes? 9 students b. How many students are enrolled in tap or ballet? 28 + 25 + 9 + 17 + 29 +25 133 students c. How many students are enrolled in jazz and ballet, but not tap? 25 students Thursday, November 6, 14
39. 39. Problem Set Thursday, November 6, 14
40. 40. Problem Set p. 101 #1-31 odd, 41 “Lack of money is no obstacle. Lack of an idea is an obstacle.” - Ken Hakuta Thursday, November 6, 14
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