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+ Inductive & Deductive Reasoning
Mr. Smith IM3
+
Inductive reasoning uses patterns to arrive at a conclusion (conjecture). It goes from specific to general.
Deductive reasoning uses facts, rules, definitions or properties to arrive at a conclusion. It goes from general to specific.
Inductive & Deductive Reasoning
+ Deductive Reasoning
n Deductive reasoning starts with a premise, which we accept to be true. Then, from that rule, we make a conclusion about something specific.
n Example:
- All turtles have shells
- The animal I have captured is a turtle
- I conclude that the animal in my bag has a shell
+ Deductive Reasoning
n A conclusion reached with deductive reasoning is logically sound, and airtight, assuming the premise is true.
n The strength of deductive reasoning is that conclusions derived with it are fully certain.
n The weakness, which was illustrated in the most recent example, is that no new information is added.
+ Inductive Reasoning
n Inductive reasoning is making a conclusion based on a set of experiences or data. If I observe that something is true many times, concluding that it will be true in all instances is a use of inductive reasoning.
n Example:
- All sheep that I've seen are white
- All sheep must be white
+ Inductive Reasoning
n The strength of inductive reasoning is that new information came be stated.
n The weakness is that the new information cannot be proven.
+Examples of Inductive Reasoning
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.
+ Examples of 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 sophomores.
+
60◦
x
Triangle sum property - the sum of the angles of any triangle is always 180°. Therefore, angle x = 30°
What is the measure of angle x?
Inductive & Deductive Reasoning
+
What is the next shape in the sequence?
Inductive & Deductive Reasoning
+
90% of humans are right handed. Joe is human, therefore Joe is right handed.
DEDUCTIVE
Inductive or Deductive?
+
You are a good student. You get all A’s. Therefore your friends must get all A’s too.
INDUCTIVE
Inductive or Deductive?
+
All oranges are fruits. All fruits grow on trees. Therefore, all oranges grow on trees.
DEDUCTIVE
Inductive or Deductive?
+
Mikhail hails from Russia and Russians are tall, therefore Mikhail is tall.
INDUCTIVE
Inductive or Deductive?
Inductive or Deductive?
Since all men are mortal, and Socrates is a man, Socrates is mortal.
DEDUCTIVE
Inductive or Deductive? Exploration of the surface
of Mars has produced some surprising facts. Therefore exploration of the surface of Jupiter will produce some surprising facts.
INDUCTIVE
Inductive or Deductive?
Since Chris is a Star Wars fan, Chris's sister must be a Star Wars fan also.
INDUCTIVE
Inductive or Deductive?
The sun is a star; the sun has planets; therefore some stars have planets.
DEDUCTIVE
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