Logical Deduction Practice — If-Then Reasoning

Practice bank for conditional logic questions in UCAT Decision Making. These test your ability to apply if-then rules, contrapositives, and chained conditionals.

---

Quick-Reference: Conditional Logic

Form	Name	Valid?
If P then Q. P is true. Therefore Q.	Modus ponens	Yes
If P then Q. Q is false. Therefore not P.	Modus tollens (contrapositive)	Yes
If P then Q. Q is true. Therefore P.	Affirming the consequent	NO
If P then Q. P is false. Therefore not Q.	Denying the antecedent	NO

Key Equivalences

• "All A are B" = "If A, then B"
• "P only if Q" = "If P, then Q"
• "P unless Q" = "If not Q, then P"
• Contrapositive of "If P then Q" = "If not Q, then not P" (always valid)
• Converse of "If P then Q" = "If Q then P" (NOT necessarily valid)
• Inverse of "If P then Q" = "If not P then not Q" (NOT necessarily valid)

Chaining Conditionals