Conditional Statements in Reasoning: If-Then Rules, Contrapositive and Unless Questions for SSC

A conditional statement has the form "If P, then Q". Questions ask what you can conclude from it, such as "If it rains, the match is cancelled. The match was not cancelled. What can you say?" These conditional statements reasoning tricks for SSC explain the one valid rule (the contrapositive), the invalid ones (converse and inverse), and the words only if and unless.

Basic Form

"If P, then Q" means that whenever P is true, Q is also true. P is the condition (the "if" part), and Q is the result (the "then" part).

Valid and Invalid Deductions

Special Words

Solved Examples

Example 1. "If it rains, the match is cancelled." The match is not cancelled. What follows?
The contrapositive is: if the match is not cancelled, it did not rain. So it did not rain.

Example 2. "If it rains, the match is cancelled." The match is cancelled. Did it rain?
This is affirming Q. We cannot say. No sure conclusion (the match can be cancelled for another reason).

Example 3. "If you study, you will pass." Rohan did not pass. What follows?
The contrapositive gives: Rohan did not study.

Example 4. "You will get the job only if you pass the test." Mohan got the job. What follows?
"Job only if pass" means Job → Pass. So Mohan passed the test.

Example 5. "You will fail unless you work hard." Sita did not work hard. What follows?
"Fail unless work hard" means: if not work hard, then fail. So Sita will fail.

Tips

• Write the statement as P → Q, and the contrapositive as not Q → not P.
• Do not reverse the arrow. "If P then Q" does not mean "If Q then P".
• Replace "unless" by "if not".
• "Only if" reverses the order: "Q only if P" means Q → P.

Quick Tips

• Use the contrapositive for sure deductions.
• Never reverse the arrow.
• Replace unless with if not.
• Write only if as an arrow from the result to the condition.

Quick Revision Points

• If P then Q is the same as if not Q then not P.
• The converse and the inverse are not valid.
• Unless means if not.
• Q only if P means Q → P.
• Affirming the result Q does not prove the condition P.

Practice Questions With Answers

1. If it rains, the match is cancelled. The match is not cancelled. What follows?
   Answer: It did not rain
2. If it rains, the match is cancelled. The match is cancelled. What follows?
   Answer: Nothing sure (it may or may not have rained)
3. If you study, you pass. Rohan did not pass. What follows?
   Answer: Rohan did not study
4. If you study, you pass. Sita passed. What follows?
   Answer: Nothing sure about her study
5. You get the job only if you pass the test. Mohan got the job. What follows?
   Answer: Mohan passed the test
6. You fail unless you work hard. Sita did not work hard. What follows?
   Answer: Sita fails
7. What is the contrapositive of "If P then Q"?
   Answer: If not Q then not P
8. Is the converse of a statement always true?
   Answer: No
9. What does "unless" mean?
   Answer: If not
10. What does "Q only if P" mean?
    Answer: If Q then P

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, read the previous topic Decision Making Reasoning and the next topic Strengthening and Weakening Arguments. Also read the Reasoning notes.

Frequently Asked Questions

What is a conditional statement?

It is a statement of the form "If P, then Q".

What is the contrapositive?

It is the statement "If not Q, then not P", which is always equal to the original.

What is the converse?

It is the reversed statement "If Q, then P", which is not always true.

What is the inverse?

It is the statement "If not P, then not Q", which is not always true.

What does unless mean?

It means "if not".

What does only if mean?

"Q only if P" means that P is necessary for Q, so Q → P.

If P → Q and Q is true, is P true?

Not necessarily.

If P → Q and Q is false, is P false?

Yes, by the contrapositive.

Is this topic asked in SSC exams?

It appears in some SSC and other reasoning papers as a type of logical reasoning.

How much time should I take?

About 30 seconds.

What are common mistakes?

Using the converse and the inverse as if they were true.

How can I practise?

Write 10 everyday if-then sentences and write their contrapositives.