MATH LESSON 1 (INDUCTIVE AND DEDUCTIVE REASONING)

Science of correct thinking

Logic

Science of correct thinking. Helps examine ideas, identify valid arguments, and draw reasonable conclusions. In mathematics it is essential because it allows us to accurately prove statements, analyze patterns, and solve problems

Logic

Helps examine ideas, identify valid arguments, and draw reasonable conclusions.

Logic

In mathematics it is essential because it allows us to accurately prove statements, analyze patterns, and solve problem

Logic

Mental process of drawing conclusions from given facts or observation

Reasoning

Is a sentence that express a complete thought and can be eiher true or false

Statement

Is the part of statement that proposes an initial condition or assumption

Hypothesis

Is the result or outcome based on the hypothesis

Conclusion

Is an unproven statement based on observed patterns or examples

Conjecture

A type of reasong based on repeated observations, and is characterized by drawing a conclusion called a conjecture from observations of specific examples

Inductive Reasoning

This type of reasoning is based on observations

Inductive Reasoning

Is a single example that disproves a conjecture

Counterexample

Specific to Broad

Inductive Reasoning

A type of reasoning that uses general facts, definitions, and a accepted properties in a logical sequence to create a sound argument

Deductive Reasoning

Broad to Specific

Deductive Reasoning

Type of reasoning that based on general facts and definitions

Deductive Reasoning

What are the Three Laws

Law of Detachment

Law of Contrapositive

Law of Syllogism

If a condition statement ( p → q ) is true and its hypothesis (p) is true, then the conclusion (q) is also true

Law of Detachment

What is Law of Detachment?

If a condition statement ( p → q) is true and its hypothesis (p) is true, then the conclusion (q) is also true

Law of Detachment in Symbols

p → q (T)

p (T)

___________

• q (T)

• •

If a conditional statement ( p → q ) is true and the conclusion (q) is false, then the hypothesis (p) must be also false

Law of Contrapositive

What is Law of Contrapositive?

If a conditional statement ( p → q ) is true and the conclusion (q) is false, then the hypothesis (p) must be also false

If the conclusion of the first conditional statement is the hypothesis of the second, then the first hypothesis implies that the conclusion of the second statement will be true

Law of Syllogism

What is Law of Syllogism?

If the conclusion of the first conditional statement is the hypothesis of the second, then the first hypothesis implies that the conclusion of the second statement will be true

The Law of Syllogism is also called

Law of Transitivity

Law of Syllogism in Symbols

p → q

q → r

_________

• p → r

• •

Law of Contrapositive in Symbols

p → q (T)

≈ q (F)

____________

• ≈ p (F)

• •

Symbol of conclusion

q

Symbol of hypothesis

p