🧩 Conditional Logic Quiz: If-Then and Contrapositives

🧩 Analytical Reasoning · Quiz 007

An if-then rule guarantees its consequence only when its condition is met. The contrapositive is valid, but reversing the rule without support is not.

Learning goalApply conditionals in the valid direction, use contraposition, distinguish converse reasoning, and interpret necessary conditions.

  • 5 questions
  • Foundation
  • Explanations after finishing
Answered 0/5
FoundationIf P is true, then Q is true. P is true. What must follow?
Need a small nudge?

The condition in the if-part has been met.

UnderstandingIf a card is red, then it is square. Card X is not square. What must be true about X?
Need a small nudge?

Use the contrapositive: not square implies not red.

ApplicationIf a bus is express, then it stops at fewer than five stations. Bus Z stops at fewer than five stations. Can we conclude that Z is express?
Need a small nudge?

The premise supplies express -> fewer stops, not fewer stops -> express.

InterpretationA valid ticket is required to enter the exhibit. Which statement correctly represents this requirement?
Need a small nudge?

A required condition must be present whenever entry occurs.

ConnectionThe rules are P -> Q and Q -> R. R is false. Which conclusion must be true?
Need a small nudge?

Apply contraposition backward through both links.

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