G8 Math Q2- Week 9- Inductive and Deductive Reasoning.ppt

Education

1. Inductive
vs.
Deductive
Reasoning

2. Deductive vs. Inductive
Reasoning
The difference:
inductive reasoninguses patterns to
arrive at a conclusion (conjecture)
deductive reasoninguses facts, rules,
definitions or properties to arrive at
a conclusion.

3. •Inductive reasoning -Think of it like a
We start with specifics and move to generalities
•Deductive reasoning –think of it like a
We start with generalities and move to specifics.

4. InductiveReasoning,involvesgoingfroma
seriesofspecificcasestoageneral
statement.Theconclusioninan
inductiveargumentisneverguaranteed.
Example:Whatisthenextnumberinthe
sequence6,13,20,27,…
Thereismorethanonecorrectanswer.

5. Here’s the sequence again 6, 13, 20, 27,…
Look at the difference of each term.
13 –6 = 7, 20 –13 = 7, 27 –20 = 7
Thus the next term is 34, because 34 –27 = 7.

6. Examples of Inductive Reasoning
Some examples
1)Every quiz has been easy. Therefore, the
test will be easy.
2)The teacher used PowerPoint in the last
few classes. Therefore, the teacher will
use PowerPoint tomorrow.
3)Every fall there have been hurricanes in
the tropics. Therefore, there will be
hurricanes in the tropics this coming fall.

7. Deductive Reasoning
Deductive Reasoning–A type of logic in which
one goes from a general statement to a
specific instance.
The classic example
All men are mortal.(major premise)
Socrates is a man.(minor premise)
Therefore, Socrates is mortal. (conclusion)
The above is an example of a syllogism.

8. Syllogism:Anargumentcomposedof
twostatementsorpremises(the
majorandminorpremises),followed
byaconclusion.
Foranygivensetofpremises,ifthe
conclusionisguaranteed,the
argumentsissaidtobevalid.

9. Iftheconclusionisnotguaranteed(at
leastoneinstanceinwhichthe
conclusiondoesnotfollow),the
argumentissaidtobeinvalid.
BECARFEUL,DONOTCONFUSE
TRUTHWITHVALIDITY!

10. Examples:
1.All students eat pizza.
Claire is a student at Wawa NHS.
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.

11. 3.Allmathteachersareover7feettall.
Mr.D.isamathteacher.
Therefore,Mr.Disover7feettall.
Theargumentisvalid,butiscertainlynot
true.
Theaboveexamplesareoftheform
Ifp,thenq.(majorpremise)
xisp.(minorpremise)
Therefore,xisq.(conclusion)

12. Deductive Reasoning
The catalog states that all entering
freshmen must take a mathematics
placement test.
Conclusion: You will have to take a
mathematics placement test.
You are an entering
freshman.
An Example:

13. Inductive or Deductive Reasoning?
Geometry example…
What is the next shape in the sequence?

14. 90% of humans are right
handed. Joe is human,
therefore Joe is right
handed.
DEDUCTIVE

15. You are a good student.
You get all A’s
Therefore your friends
must get all A’s too
INDUCTIVE

16. All oranges are fruits.
All fruits
grow on trees
Therefore, all oranges
grow on trees
DEDUCTIVE

17. Mikhail hails from
Russia and Russians are
tall, therefore Mikhail is
tall
INDUCTIVE