Conditional Logic

Conditional statements — "if...then" reasoning — are fundamental to the UCAT Decision Making subtest. They underpin syllogisms, logical puzzles, and assumption questions. This lesson teaches you the four related forms of any conditional statement, which transformations are logically valid, and how to apply this knowledge to UCAT questions rapidly and accurately.

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The Basic Conditional

A conditional statement has the form:

If P, then Q.

Where:

• P is the antecedent (the "if" part)
• Q is the consequent (the "then" part)

Examples

Conditional	P (antecedent)	Q (consequent)
If it rains, the ground gets wet.	It rains	The ground gets wet
If a patient has Type 1 diabetes, they require insulin.	Patient has Type 1 diabetes	They require insulin
If you score above 700, you will be invited to interview.	Score above 700	Invited to interview

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The Four Related Forms

Every conditional "If P, then Q" has three related statements. Understanding which are valid and which are invalid is essential.