Conditional Statements Cheat Sheet

Conditional Statements Cheat Sheet

Quick Revision

A conditional statement has the form "If P, then Q". From it you can build three related statements — and only one of them always has the same truth as the original.

1. The Four Forms

Statement       : If P, then Q
Converse        : If Q, then P
Inverse         : If not P, then not Q
Contrapositive  : If not Q, then not P

2. What Is Equivalent

• The contrapositive is always logically equivalent to the statement — if one is true, so is the other.
• The converse and the inverse are not equivalent to the statement (though they are equivalent to each other).

3. Necessary and Sufficient

In "If P, then Q":

• P is sufficient for Q — P alone guarantees Q.
• Q is necessary for P — P cannot happen without Q.

4. Worked Example

Statement: "If it rains, the match is cancelled."

Contrapositive : If the match is not cancelled, it did not rain.  (true — same meaning)
Converse       : If the match is cancelled, it rained.            (not guaranteed)

The match might be cancelled for another reason, so the converse need not hold.

5. Exam Quick Tips

• To test a conditional, use its contrapositive — it is always safe.
• "P only if Q" means If P, then Q, not the reverse.
• Do not assume the converse is true; that is the most common trap.

Keep revising with the rest of the Reasoning section:

• All Reasoning topics
• Assertion and Reason Cheat Sheet
• Statement and Arguments Cheat Sheet

How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.