Section 2.2: Deductive and Inductive Reasoning

Section 2.2: Deductive and Inductive Reasoning

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Inductive Reasoning

Using patterns to make conjectures

​The following picture shows a pattern.

Multiple Choice

What is the next figure in the pattern?

​The following shows a number pattern.

Fill in the Blank

Fill in the next number in the pattern

0, 2, 6, 12, 20, ...

Open Ended

What is the next letter in the sequence?

J, F, M, A, M, J, J, A,

COUNTEREXAMPLE

Proves a conjecture wrong

Conjecture: All dogs are hairy.

COUNTEREXAMPLE: The Argentine Pila Dog is hairless.

Open Ended

What is a counterexample for the conjecture:

All months have 31 days

Open Ended

Give a counterexample for the statement:

The sum of 2 odd numbers is always odd.

DEDUCTIVE REASONING

There are 2 types of Deductive Reasoning

• Law of Detachment

• Law of Syllogism

• https://www.youtube.com/watch?v=YBNrkXEqCiI

Deductive Reasoning

uses laws, facts, definitions, rules, etc.

Consider the sentence:
If I don't understand, then I will ask questions.

The BLUE "if" section is what we will call part "A".

The RED "then" section is what we will call part "B".

Multiple Choice

Which is the "A" section in this statement?

If it is cold, then I wear glove.

• if it is cold

• then I wear gloves

• I don't like to be cold

• it was cold yesterday

Multiple Choice

Which is the "B" section in this statement?

If it is cold, then I wear glove.

• if it is cold

• then I wear gloves

• I don't like to be cold

• it was cold yesterday

Both DETACHMENT and SYLLOGISM will start with a sentence in this form.

The sentence that follows determines if you can use detachment, syllogism, or neither.

To use detachment, the next sentence has to restate the "A" section.

Note: You don't have to restate the "A" section word for word, just the general idea.

You would then conclude the "B" section.

Multiple Choice

What can you conclude using detachment?

If I have a dog, then I have to take it out for walks. I have a Poodle (type of dog).

• Conclusion: Poodles are cute.

• Conclusion: I like taking my dog for walks.

• Conclusion: I have to take my dog out for walks.

Open Ended

What can you conclude using detachment?

If it is after 9pm, then I am in the bed. It is 9:30 pm.

Both DETACHMENT and SYLLOGISM will start with a sentence in this form.

The sentence that follows determines if you can use detachment, syllogism, or neither.

To use syllogism, the next sentence has to start with the "B" section and also has to give a new "then" section, which we will call part "C".

The green is the new then ("C") section.

You would then conclude the "A" and the "C" section in a new if-then sentence.

The "B" sections that are both the end and beginning of a sentence are canceled.

Multiple Choice

What can you conclude using syllogism?

If I exercise, then I will be healthy. If I am healthy, then I will be happy.

• Exercising makes you happy.

• Conclusion: If I exercise, then I will be happy.

• If i am happy, then I exercised.

If these patterns are not followed, you cannot make a valid conclusion.

Multiple Choice

Is the conclusion is based on inductive or deductive reasoning?

Students at Olivia’s high school must have a B average in order to participate in sports. Olivia has a B average, so she concludes that she can participate in sports at school.

• inductive

• deductive

Multiple Choice

Is the conclusion is based on inductive or deductive reasoning?

Holly notices that every Saturday, her neighbor mows his lawn. Today is Saturday. Holly concludes her neighbor will mow his lawn.

• inducutive

• deductive