Hard
conditional-logicif-thenmodus-ponens

What Can Be Concluded From These Conditional Statements?

Problem Statement

Given: If it rains, the game is cancelled. If the game is cancelled, refunds are issued. It is raining. What must be true? A) Refunds are issued. B) The game might still happen. C) It's not raining. D) No conclusion can be drawn.

Answer

A) Refunds are issued

Step-by-Step Explanation

  1. 1

    Let's use conditional logic notation:

  2. 2

    Statement 1: Rain → Game cancelled

  3. 3

    Statement 2: Game cancelled → Refunds issued

  4. 4

    Given fact: It is raining

  5. 5

    Step 1: Since it's raining, and Rain → Game cancelled, the game IS cancelled.

  6. 6

    Step 2: Since the game is cancelled, and Game cancelled → Refunds issued, refunds ARE issued.

  7. 7

    This is called a 'chain of conditionals' or 'hypothetical syllogism.'

  8. 8

    Rain → Game cancelled → Refunds issued

  9. 9

    Since Rain is true, we can conclude Refunds are issued.

  10. 10

    Option A is correct.

  11. 11

    This demonstrates modus ponens applied twice.