Deductive and Inductive Reasoning: Valid and Invalid Arguments, Modus Ponens, Modus Tollens and Examples for SSC Exams

All logical reasoning questions depend on two basic types of thinking: deduction and induction. This guide on deductive and inductive reasoning for SSC explains the difference between them, the meaning of valid and sound arguments, the standard forms of valid deduction (modus ponens, modus tollens and others) and the common wrong forms, with solved examples, practice questions and FAQs.

Argument, Premise and Conclusion

An argument is a group of statements in which the premises are given as the reasons to accept the conclusion. Words like therefore, thus, hence, so, consequently usually introduce the conclusion; words like because, since, as, for introduce the premises.

Deductive, Inductive and Abductive Reasoning

Validity and Soundness

An argument can be valid but unsound: “All fish can fly; a shark is a fish; so a shark can fly” is valid in form but its premise is false, so it is not sound.

Valid Forms of Deductive Reasoning

Invalid Forms (Fallacies of Form)

Inductive Reasoning: Types

• Generalisation: from a sample to the whole group. It is stronger when the sample is large, random and representative.
• Analogy: if two things are alike in many ways, they may be alike in another way. It is stronger when the similarities are relevant and many.
• Causal inference: concluding that A is the cause of B from the observed pattern; it is weak if there may be another cause (see the post hoc fallacy).
• Prediction: from the past events to the future events.

Solved Examples

Example 1. All doctors are graduates. Rohan is a doctor. Therefore Rohan is a graduate. What kind of reasoning is this?
Deductive, and it is valid.

Example 2. Every crow that I have seen is black. So all crows are black. What kind of reasoning is this?
Inductive; the conclusion is only probable.

Example 3. If a number is divisible by 6, it is divisible by 3. 14 is not divisible by 3. What can be concluded?
By modus tollens, 14 is not divisible by 6.

Example 4. If the alarm rings, the guard wakes up. The guard woke up. So the alarm rang. Is this valid?
No, it is the fallacy of affirming the consequent.

Example 5. If it is Monday, the shop is closed. The shop is open. What follows?
By modus tollens, it is not Monday.

Tips for the Exam

• Ask whether the conclusion is certain (deduction) or only probable (induction).
• Judge validity on the basis of the given statements only, even if they are factually wrong.
• Do not confuse the converse (If Q then P) with the original statement (If P then Q).
• The contrapositive (If not Q then not P) is always equivalent to the original statement.

Quick Tips

• Judge validity from the form and not from the facts.
• Remember that modus tollens uses the contrapositive.
• Do not affirm the consequent.
• Remember that induction gives only a probable conclusion.

Quick Revision Points

• Deduction goes from general to specific; induction from specific to general.
• A valid argument with true premises is sound.
• Modus ponens: P → Q, P, so Q.
• Modus tollens: P → Q, not Q, so not P.
• Affirming the consequent is a fallacy.

Practice Questions With Answers

1. Which reasoning moves from the general to the specific?
   Answer: Deductive reasoning
2. Which reasoning gives only a probable conclusion?
   Answer: Inductive reasoning
3. If P then Q; P is true. What follows?
   Answer: Q (modus ponens)
4. If P then Q; Q is false. What follows?
   Answer: P is false (modus tollens)
5. What is a valid argument with true premises called?
   Answer: A sound argument
6. If it rains, the match is cancelled. The match is cancelled. Does it follow that it rained?
   Answer: No (affirming the consequent)
7. If a figure is a square, it has four sides. A figure has four sides. Is it a square?
   Answer: Not necessarily
8. Which word usually introduces a conclusion: therefore or because?
   Answer: Therefore
9. What is the contrapositive of If P then Q?
   Answer: If not Q then not P
10. What is the strongest type of inductive generalisation based on?
    Answer: A large, random, representative sample

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Logical Reasoning notes page and the next topic Logical Fallacies and Common Reasoning Errors.

Frequently Asked Questions

What is deductive reasoning?

Reasoning from general statements to a specific conclusion that must be true if the premises are true.

What is inductive reasoning?

Reasoning from specific observations to a general conclusion that is probable.

What is a valid argument?

An argument in which the conclusion follows necessarily from the premises.

What is a sound argument?

A valid argument whose premises are all true.

What is modus ponens?

If P then Q; P; therefore Q.

What is modus tollens?

If P then Q; not Q; therefore not P.

What is the fallacy of affirming the consequent?

Concluding P from If P then Q and Q.

What is a premise?

A statement given as a reason to accept the conclusion.

Can a valid argument have a false conclusion?

Yes, if one of its premises is false.

Is this topic asked in SSC?

Yes. It is the base of the statement and conclusion questions.

What is abductive reasoning?

Reasoning to the best explanation of the observations.

What is the converse of If P then Q?

If Q then P, which is not equivalent.