[AGE4 00] Lesson 6: Elementary Logic Inductive and Deductive Reasoning

Inductive Reasoning 

• It is a type of reasoning that uses specific examples to reach a general conclusion.

• Conjecture 

  • The conclusion formed by using inductive reasoning.

  • It is an idea that may or may not be correct.

• Use inductive reasoning to predict the next number of the pattern below.

  • A. 5, 10, 15, 20, 25, ____.

  • B. 1, 4, 9, 16, 25, ____.

Conjecture

• The conclusion formed by using inductive reasoning.

• It is an idea that may or may not be correct.

Counterexample

• It is a method that disproves a conjecture.

• It is an example for which the conjecture is incorrect.

• To prove the conjecture is false.

Deductive Reasoning 

• It is a type of reasoning that uses general procedures and principles to reach a conclusion.

• It is the process of reaching a general conclusion by applying general assumptions, procedures, or principles.

Some Generalized Principles

• PEMDAS

• Property of Real Numbers 

• Property of Inequality 

• Postulates 

• Theorems

Logic Puzzle

They can be solved by using deductive reasoning and a chart that enables us to display the given information in a visual manner.

Inductive

• Reaching conclusions based on a series of observations.

• Conjecture may or may not be valid or uncertain.

Deductive

• Reaching conclusions based on previously known facts.

• Conjecture are correct and valid or certain.

Forms of Deductive Reasoning

1. Hypothetical Syllogism

2. Categorical Syllogism

Hypothetical Syllogism 

It is a type of deductive reasoning consisting of a conditional major premise, an unconditional minor premise, and an unconditional conclusion.

Types of Hypothetical Syllogism

1. Modus Ponens

2. Modus Tollens 

Modus Ponens

• It is a hypothetical syllogism with the form:

If p then q,

and p,

Therefore, q.

where p and q are distinct statements.

Modus Tollens

• It is a hypothetical syllogism with the form: 

If p then q,

and ¬q,

Therefore, ¬p.

where p and q are distinct statements.

Categorical Syllogism 

• It is a form of deductive reasoning wherein a categorical conclusion is based on two categorical premises.

• There are four types of propositions.

4 Types of Propositions in Categorical Syllogism

1. Positive Universal

2. Negative Universal

3. Positive Existential

4. Negative Existential

Positive Universal

• “All are…” (A)

• All A are B. 

• Ex. All dogs are mammals. 

Negative Universal 

• “None are…” (E)

• No A are B. 

• Ex. No dogs are fish. 

Positive Existential 

• “Some are…” (I)

• Some A are B. 

• Ex. Some dogs are born.

Negative Existential 

• “Some are not…” (O)

• Some A are not B.

• Ex. Some dogs are not brown.

3 types of propositions to create an argument in Categorical Syllogism

1. Major Premise (Universal Quantifier) 

2. Minor Premise (Existential Quantifier) 

3. Conclusion (Universal or Existential) 

4. It is denoted by: 

All p are q.

r is p.

Therefore, r is q.

• Example: 

All fish are sea creatures.

Every shark is a fish.

Therefore, every shark is a sea creature. 

Major Premise

Universal Quantifier

Minor Premise

Existential Quantifier

Conclusion

Universal or Existential