1. DEE: If you think we're wax-works, you ought to pay, you know. Wax-works weren't made to be looked at for nothing. Nohow. DUM: Contrariwise, if you think we're alive, you ought to speak. DUM: I know what you're thinking about, but it isn't so, nohow. DEE: Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.

2. MA 110: Finite Math Dr. Maria Byrne Instructional Laboratory 0345 Lecture 1/21/2009 Homework: 1.2: 1-21 odd (Skip 7c, 9c); (36 for a BP) Due Monday 1/26

3. Today We Will 1.Collect Homework 1.1 2.Begin 1.2 Symbolic Logic We will learn about : Statements Negations Compound Statements

4. 1.2 Symbolic Logic Symbolic logic involves the use of symbols to represent the quantities and relationships of statements. These quantities and relationships are abstracted away from their original content.

5. A Statement A statement is a sentence that can be objectively determined TRUE or FALSE. A statement is denoted by a lowercase letter, usually p, r or s. A statement can be identified by whether or not it can be assigned a truth value.

6. A Statement A statement is a sentence that can be objectively determined TRUE or FALSE. A statement is denoted by a lowercase letter, usually p, q or r. A statement can be identified by whether or not it can be assigned a truth value.

7. A Statement A statement is a sentence that can be objectively determined TRUE or FALSE. A statement is denoted by a lowercase letter, usually p, r or s. A statement can be identified by whether or not it can be assigned a truth value.

8. Identifying Statements

9. Abraham Lincoln was the best president.

10. Opinion Not a statement.

11. Abraham Lincoln was the best president. Opinion Not a statement.

12. 2+2=4

13. Is a statement.

14. 2+2=5

15. Is a statement.

16. It is a lousy day.

17. Opinion. Not a statement.

18. There are exactly 100,400,327 stars in the universe.

19. Is a statement.

20. How many stars are in the universe?

21. Question. Not a statement.

22. The sun will rise tomorrow.

23. Is a statement.

24. Grab that fish!

25. Instructions Not a statement.

26. Ouch!

27. Not a statement.

28. "Socrates is a man.”……………………………. Statement "A triangle has three sides.”…………………… Statement "Paris is the capital of England.”………………. Statement "Who are you?”……………………………… Question "Run!"………………………………………… Instuction "I had one grunch but the eggplant over there.”.. Nonsense "Red is a pretty color.”………………………… Opinion “This is not a statement.”……………………… Paradox Classify the sentences below:

29. "Socrates is a man.”……………………………. Statement "A triangle has three sides.”…………………… Statement "Paris is the capital of England.”………………. Statement "Who are you?”……………………………… Question "Run!"………………………………………… Instruction "I had one grunch but the eggplant over there.”.. Nonsense "Red is a pretty color.”………………………… Opinion “This is not a statement.”……………………… Paradox Classify the sentences below:

30. "Socrates is a man.”……………………………. Statement "A triangle has three sides.”…………………… Statement "Paris is the capital of England.”………………. Statement "Who are you?”……………………………… Question "Run!"………………………………………… Instruction "I had one grunch but the eggplant over there.”.. Nonsense "Red is a pretty color.”………………………… Opinion “This is not a statement.”……………………… Paradox Classify the sentences below:

31. Negations (Not not negations)

32. Negation The negation of a statement p is the statement q that is a denial of the statement p. A denial has the opposite truth value of p. The symbol for the negation is: ~

33. Negation The negation of a statement p is the statement q that is a denial of the statement p. A denial has the opposite truth value of p. The symbol for the negation is: ~

34. Negation The negation of a statement p is the statement q that is a denial of the statement p. A denial has the opposite truth value of p. The symbol for the negation is: ~

35. Statement: Her dress is red. Negation: Her dress is not red. Example

36. Statement: Her dress is red. Negation: Her dress is not red. Example

37. Statement: Today is January 21st. Negation: Today is not January 21st. Example

38. Statement: Today is January 21st. Negation: Today is not January 21st. Example

39. Statement: Today is January 21st. Negation: Today is not January 21st. Example Statement: True (T) Negation: False (F)

40. Statement: Lizards are mammals. Negation: Lizards are not mammals Example

41. Statement: Lizards are mammals. Negation: Lizards are not mammals Example

42. Statement: Lizards are mammals. Negation: Lizards are not mammals Example Statement: False (F) Negation: True (T)

43. Statement: We are not mice. Negation: We are not not mice. Example

44. Statement: We are not mice. Negation: We are not not mice. Example

45. Statement: We are not mice. Negation: We are not not mice. Example ____________

46. Statement: We are not mice. Negation: We are not not mice. Example ____________ mice.

47. Statement: We are not mice. Negation: We are not not mice. Example ____________ mice. Statement: True (T) Negation: False (F)

48. The Negation of a Negation “Not not p” is “p” In symbols: to class

49. “It is not the case that” Always negates a sentence. Her dress is red. –Negation: It is not the case that her dress is red. We are mice. –Negation: It is not the case that we are mice.

50. “It is not the case that” Always negates a sentence. Her dress is red. –Negation: It is not the case that her dress is red. We are mice. –Negation: It is not the case that we are mice.

51. “It is not the case that” Always negates a sentence. Her dress is red. –Negation: It is not the case that her dress is red. We are mice. –Negation: It is not the case that we are mice.

52. “It is not the case that” Always negates a sentence. Her dress is red. –Negation: It is not the case that her dress is red. We are mice. –Negation: It is not the case that we are mice.

53. “It is not the case that” Always negates a sentence. Her dress is red. –Negation: It is not the case that her dress is red. We are mice. –Negation: It is not the case that we are mice.

54. “It is not the case that” Always negates a sentence. Her dress is red. –Negation: It is not the case that her dress is red. We are mice. –Negation: It is not the case that we are mice.

55. “It is not the case that” Always negates a sentence. Her dress is red. –It is not the case that her dress is red. We are mice. –It is not the case that we are mice.

56. Equivalent Ways to Negate Negations of “We are not mice.” 1. We are mice. 2. It is not the case that we are not mice.

57. Equivalent Ways to Negate Negations of “We are not mice.” 1. We are mice. 2. It is not the case that [we are not mice].

58. Equivalent Ways to Negate Negations of “We are not mice.” 1. We are mice. 2. It is not the case that [we are not mice]. 3. To class.

59. Equivalent Statements If two statements have the same meaning, we say that they are equivalent. If p is equivalent to q, we write p ≡ q

60. Tricky Negation Statement: Some cats have tails.

61. Tricky Negation Statement: Some cats have tails. Negation: It is not the case that some cats have tails.

62. Tricky Negation Statement: Some cats have tails. Negation: It is not the case that some cats have tails. What does this mean?

63. Tricky Negation Statement: Some cats have tails. Negation: It is not the case that some cats have tails. What does this mean? No cat has a tail!

64. Negate the Following Sentences Some of the beverages contain caffeine. Some of the fruits are not red. All candy promotes tooth decay.

65. Compound Statements

66. Compound statements are statements connected by AND, OR or “IF … THEN”

67. Compound Statements Compound statements are statements connected by AND, OR or “IF … THEN” p AND q p OR q IF p, THEN q.

68. Conjunction AND The conjunction of p and q is “p AND q”. Symbolized by:  Example: p: I’m a dog. q: You’re a cat. p  q: I’m a dog and you’re a cat.

69. Disjunction OR The disjunction of p and q is “p OR q”. Symbolized by:  Example: p: I’m a dog. q: You’re a cat. p  q: I’m a dog or you’re a cat.

70. Conditional IF…THEN The condition of p and q is “IF p THEN q”. Symbolized by:  Example: p: I’m a dog. q: You’re a cat. p  q: If I’m a dog then you’re a cat.

71.  

72.   AND OR