1. Inductive Reasoning
Drawing a conclusion based upon repeated observations

2. Deductive Reasoning
Drawing a conclusion based upon facts or rules and NOT repeated observations

3. Four times, John was late to class and four times his teacher gave him a detention
John was late to class again today
Conclusion: John will get a detention
This conclusion was based on INDUCTIVE reasoning

4. One of the class rules is that anyone who is late will receive a detention
John was late to class
Conclusion: John will get a detention
This conclusion was based on DEDUCTIVE reasoning

5. In the first inning of a baseball game, Dave Mover of the Adirondack Avalanche struck out. The next inning the coach benched him. In the second inning, Scott Sponsor struck out. The next inning the coach benched him. In the third inning, Mike Disoda struck out. The next inning the coach benched him. In the fourth inning, Cohen Suzuki struck out.
Conclusion:
The next inning, the coach benched him.
This conclusion was made using ___________ reasoning
inductive

6. If you strike out, then in the next inning you will get benched
This sign hangs in the Appalachia Apple Pickers baseball team’s locker room.
If you strike out, then in the next inning you will get benched
In the first inning, Adam struck out
Conclusion:
The next inning, the coach benched him.
This conclusion was made using ___________ reasoning
deductive

7. The Law of Detachment
You are told that a given conditional statement is true
You are told that the hypothesis of the conditional statement is true.
Therefore you can conclude that the conclusion is also true

8. The Law of Detachment If a car is out of gas, then it will not start
Sarah’s car is out of gas
Therefore Sarah’s car will not start

9. The Law of Detachment YES
If two angles form a linear pair, then their noncommon sides are opposite rays
YES A D E B

10. The Law of Detachment NO
If Mika goes to the beach, then she will wear sunscreen
Mika is wearing sunscreen
Can we conclude that Mika is at the beach? NO

11. The Law of Syllagism
If a, then b
If b, then c
Therefore, if a, then c

12. The Law of Syllagism

13. The Law of Syllagism If you get a job, then you will earn money
If you earn money, then you will buy a car
If you get a job, then you will buy a car

14. The Law of Syllagism Here’s why
If you eat food in the hallway, then my kids will go to jail
Here’s why

15. Law of Syllogism
If you eat food in the hallway, then you will spill something on the floor
If you spill something on the floor, someone will slip and fall.

16. Law of Syllogism
If you spill something on the floor, someone will slip and fall
If someone slips and falls, then they will sue the school

17. Law of Syllogism
If someone slips and fall, then they will sue the school
If someone sues the school, then the school will have to pay them a lot of money

18. Law of Syllogism
If someone sues the school, then the school will have to pay them a lot of money
If the school has to pay someone a lot of money, then the school will blame me for not stopping someone from eating in the hall

19. Law of Syllogism
If the school has to pay someone a lot of money, then they will blame me for not stopping someone for eating in the hall
If the school blames me for not stopping someone from eating in the hall, then I will get upset.

20. Law of Syllogism
If the school blames me for not stopping someone from eating in the hall, then I will get upset
If I get upset, then someone is going to record me being upset

21. Law of Syllogism
If I get upset, then someone will record me being upset
If someone records me being upset, then they will post the recording on youtube.

22. Law of Syllogism
If someone records me being upset, then they will post the recording on youtube.
If someone posts a video of me being upset, then everyone in the world will be able to watch it

23. Law of Syllogism
If someone posts a video of me being upset, then everyone in the world will be able to watch it
If everyone in the world is able to watch the video of me being upset, then my kids will be too embarrassed to go to school.

24. Law of Syllogism
If everyone in the world is able to watch the video of me being upset, then my kids will be too embarrassed to go to school.
If my kids are too embarrassed to go to school, then they will never get a high school diploma.

25. Law of Syllogism
If my kids are too embarrassed to go to school, then they will never get a high school diploma
If my kids never get a high school diploma, then they will never go to college.

26. Law of Syllogism
If my kids never get a high school diploma, then they will never go to college
If my kids don’t go to college, then they will not get the kind of job that they want.

27. Law of Syllogism
If my kids don’t go to college, then they will not get the kind of job that they want.
If my kids do not get the kind of job that they want, then they will not be able to buy the things that they want.

28. Law of Syllogism
If my kids do not get the kind of job that they want, then they will not be able to buy the things that they want.
If my kids are not able to buy the things that they want, then they will just try to steal them from a store.

29. Law of Syllogism
If my kids are not able to buy the things that they want, then they will just try to steal them from a store.
If my kids try to steal the things they want from a store, then they will get caught.

30. Law of Syllogism
If my kids try to steal the things they want from a store, then they will get caught.
If my kids get caught stealing things from a store, then they will get arrested.

31. Law of Syllogism
If my kids get caught stealing things from a store, then they will get arrested.
If my kids get arrested, then they will go to trial

32. Law of Syllogism If my kids get arrested, then they will go to trial
If my kids go to trial, then they will be found guilty

33. Law of Syllogism
If my kids go to trial, then they will be found guilty
If my kids are found guilty, then they will go to jail.

34. Law of Syllogism
So…..
If you eat food in the hallway, my kids will go to jail

36. Use inductive reasoning to draw a conclusion about the probable next number in each list27 34 32

37. Use deductive reasoning to draw a conclusion about the following:
Premise: Every odd integer is followed by an even integer and every even integer is followed by an odd integer
even
odd
even
odd

38. Premise: The password for your i-tunes account must be at least six characters long, must contain only numbers and letters and must contain at least one number and one letter
1. You have a valid password. Draw three conclusions about your password
a. Your password is at least 6 characters long

39. Premise: The password for your i-tunes account must be at least six characters long, must contain only numbers and letters and must contain at least one number and one letter
1. You have a valid password. Draw three conclusions about your password
b. Your password is made up of only numbers and letters

40. Premise: The password for your i-tunes account must be at least six characters long, must contain only numbers and letters and must contain at least one number and one letter
1. You have a valid password. Draw three conclusions about your password
c. Your password contains at least one number and at least one letter

41. Premise: The password for your i-tunes account must be at least six characters long, must contain only numbers and letters and must contain at least one number and one letter
2. Which of the following are valid passwords
5nhth54 3#4$BH6 LGTFCC
K6dL9 ASd5Fg

42. Premise: May 22, 1985 was a Wednesday.
Draw a conclusion about May 23, 1985
May 23, 1985 was a Thursday

43. Premise: May 22, 1985 was a Wednesday.
Draw a conclusion about May 28, 1985
May 28, 1985 was a Tuesday

44. Premise: The Indy 500 is always run on Memorial Day
Premise: The Indy 500 is always run on Memorial Day. Memorial Day is always the last Monday in May
On what date was the Indy 500 run in 1985?
May 27, 1985

45. Be Careful When Drawing Your Conclusions

46. A four engine jet is flying from New York to Los Angeles
A four engine jet is flying from New York to Los Angeles. The estimated arrival time is 1:00 PM. When one of the engines fails, the plane slows down and the new estimated arrival time becomes 2:00 PM. A little while later, a second engine fails, causing the plane to slow down making the new arrival time 3:00 PM. A short time after that, a third engine fails, making the updated arrival time to be about 4:00 PM.
Conclusion: If the last engine fails, the plane will arrive at about 5:00 PM

47. FAT-A-WAY
Lose 15 lbs a week
Guaranteed
Conclusion: If you currently weigh 150 pounds, then in 15 weeks you will be invisible

48. Homework
Pg 7 #1 – 12
Hand In Tomorrow

49. Warm Up Predict the next multiplication fact Verify your conclusion 3715
555
Verify your conclusion

50. Determine the most probable next term in each list of numbers38 36 56

51. Determine the most probable next term in each list of numbers2

52. Predict the next equation, then verify your conjecture

53. Predict the next equation, then verify your conjecture

54. Predict the next equation, then verify your conjecture

55. Predict the next equation, then verify your conjecture

56. Predict the next equation, then verify your conjecture

57. Predict the next equation, then verify your conjecture

58. Homework
Pg 7&8 #15 – 41 odd
Hand In Tomorrow

59. Warm Up
= __ 55
5,050
1+2+3+… = __

60. Gauss Method for Finding Sums
= __ 55

61. Find each sum by using the Gauss Method of Sums
1+2+3+… =_____
1+2+3+…+2000=_____
1+2+3+… =_____
10,100
500,500
2,001,000
125,250

62. How could you modify the Gauss method to find the sum below?
1+2+3+… = ___ 5,
5,151

63. Modify the Gauss method to find the sum below.…
25 x 102
2,550

64. Modify the Gauss method to find the sum below.…
Numbers in sum: 200 ÷ 5=40
Number of pairs: 20
Sum of each pair: 205
20 x 205
=4100

65. Homework
Gauss Sum Worksheet
Hand In Tomorrow