Deductive vs. Inductive

Valid Reasoning

What’s the difference?

ICE DRIPInductive Contains ExamplesDeductive Reasoning involves proof!

Difference between True/False and Valid/Invalid!

• If a child puts his or her hand into a bag of candy and withdraws three pieces, all of which are red, he or she may conclude that all the candy is red.

1. Which of the following claims would be best expressed by inductive reasoning?

• Your first quiz grade usually indicates how you will do in the course.

• The final exam accounts for 30% of the course grade.

• Late papers will not be accepted. • Gravity's Rainbow

is required reading in your course.

2. Which of the following claims would be best expressed by deductive reasoning?

• California's population growth rate slowed last year.

• California residents appreciate their good weather.

• California residents are residents of the United States.

• More cars are registered in California than in any other state.

3. Which of the following arguments would lead to a deductive conclusion?

• There was a mild winter this year, and previously whenever there's been a mild winter the cherry crop suffers.

• The cherry crop needs at least a week of freezing temperatures for best results, and this winter the temperature stayed several degress above freezing.

• Primo noticed that whenever the skiing was good in the winter, the cherry crop was profitable, and this year the skiing was good.

• Not since 1972 have I seen a good cherry crop after a mild winter, and this winter has been mild.

All men are mortal. (major premise)

Socrates is a man. (minor premise)

Therefore, Socrates is mortal. (conclusion)

1. All students eat pizza.Claire is a student at ASU.Therefore, Claire eats pizza.

2. All athletes work out in the gym. Barry Bonds is an athlete. Therefore, Barry Bonds works out in the gym.

Valid or Invalid???

All smiling cats talk. The Cheshire Cat smiles.

Therefore, the Cheshire Cat talks.

Examples

• #6 No one who can afford health insurance is unemployed.

All politicians can afford health insurance.

Therefore, no politician is unemployed.

VALID OR INVALID?????

• 16 Some professors wear glasses. Mr. Einstein wears glasses.

Therefore, Mr. Einstein is a professor.

• What is the next number in the sequence 6, 13, 20, 27,…

This premise was succinctly reflected in the wise words of Benjamin Franklin (1706-90):

• Tell me and I forget, Teach me and I remember, Involve me and I learn.

• There are 32 books on the top-shelf of the bookcase, and 12 on the lower shelf of the bookcase. There are no books anywhere else in my bookcase. Therefore, there are 44 books in the bookcase

• Bergen is either in Norway or Sweden. If Bergen is in Norway, then Bergen is in Scandinavia. If Bergen is in Sweden, the Bergen is in Scandinavia. Therefore, Bergen is in Scandinavia.

The members of the Williams family are Susan, Nathan and Alexander.Susan wears glasses.Nathan wears glasses.Alexander wears glasses.Therefore, all members of the Williams family wear glasses.

• It has snowed in Massachusetts every December in recorded history.Therefore, it will snow in Massachusetts this coming December.

• All odd numbers are integers.All even numbers are integers.Therefore, all odd numbers are even numbers.

Valid or Invalid?

Mr. Smith owns only blue pants and brown pants. Mr. Smith is wearing a pair of his pants today. So, Mr. Smith is wearing either blue or brown pants today.

Valid or Invalid

Major Premise: All cats are mammals.Minor Premise: Fluffy is a cat. Conclusion: Therefore Fluffy is a mammal.

• I have observed a hundred catsFifty of them purred when I rubbed their heads. Fluffy is a cat. Therefore, there is a 50 percent chance that Fluffy will purr if I rub his head.

Inductive or Deductive?

I've noticed previously that every time I kick a ball up, it comes back down, so I guess this next time when I kick it up, it will come back down, too.

Inductive or Deductive?

• Newton's Law states that everything that goes up must come down. And so, if you kick the ball up, it must come down.

Valid or Invalid

• If it is six pm, then the pizza shop is open. If the pizza shop is open, then Suzan will go buy a pizza. => If it is six pm, then Suzan will go buy a pizza.

Valid or Invalid

• If it is Sunday, then it is free to park at a meter. If it is free to park at a meter, then Sheela will park at a meter. => If it is Sunday, then Sheela will park at a meter.

Valid or Invalid

• If it is Polina's birthday, then she will buy a cheesecake.

• If Polina does not buy a cheesecake, then she will buy a strawberry cream pie.

• So, if it is Polina's birthday, she will buy a strawberry cream pie.

Valid or Invalid

• If it is Saturday, then Sylvia has a lot of free time. If Sylvia has a lot of free time, then she will go shopping. => If it is Saturday, Then Sylvia will go shopping.

Valid or Invalid

• If it is Thanksgiving, Brian will buy a turkey. • If it is not Thanksgiving, Brian will buy a steak.• Therefore, If it is Thanksgiving, Brian will buy a

steak.

Valid or Invalid

•If it is Christmas, then Sylvia will buy her mom a present.

• If it is Christmas, then Sylvia will buy her brother a present.

• If Sylvia buys her mom a present, then she will buy her brother a present.

Let’s Practice!

Question 1

• If it is Halloween, Sheela will buy lots of candy. If Sheela buys lots of candy, Then she will eat all the candy. What follows?

A. If it is Halloween, Sheela will not buy lots of candy.B. If it is Halloween, Sheela will eat all the candy.C. If Sheela buys a lot of candy, Then it must be Halloween.D. If Sheela eats a lot of candy, she must buy a lot of candy.

Question 2

If it is 4th of July, There will be a parade. If thereis a parade, Polina will go to the parade. If it is4th of July, Polina will go to the parade.

A. Valid B. Invalid

Question 3

• If Sheela's sister is sick, then she needs to see the doctor. What is the other hypothesis needed to allow us to conclude: If Sheela's sister is sick, Sheela will drive her to the see the doctor.

A. If Sheela is well, she will not be going to see the doctor. B. If Sheela is sick, she will go to see the doctor. C. If Sheela's sister needs to go see the doctor, Sheela will drive her to see the doctor. D. If Sheela's sister is well, she will have dinner.

Question 4

• If Sheela studies, then she will do well on the test

• Sheela studied• So she will do well on the test

A. ValidB. Invalid

Question 5

• If Jessica stays at home, then she'll cook dinner; If she cooks dinner, then she'll make spaghetti; So if Jessica stays at home, she will make spaghetti.

• A. Valid• B. Invalid

Question 6

If it rains, Susan will be staying home; If Susan is not staying home, then it did not rain.

A. ValidB. Invalid

Question 7

If Brian does well on the job interview, then he'll get the job; He didn't get the job; So, he didn't do well on the job interview.

A. ValidB. Invalid

Question 8

State a valid conclusion:If two figures are congruent, then their areas are

equal.The area of ABCD equals the area of WXYZ

Question 9

State a valid conclusion:If the measures of two angles have a sum of 90

degrees, then the angles are complementary.m 1+ m 2 = 90∠ ∠

Question 10

State a valid conclusion:• If two lines are parallel, then they do not

intersect.• Line a is parallel to line b.

Question 11

State a valid conclusion:If three points lie on the same line, then they are

collinear.Points A, B, and C lie on line l.