If A → B, B → C, C → D, and A is false, which statement must be true?

• A. A is false
• B. B is true
• C. C is true
• D. D is true

Answer: (A)

The key idea is how implications behave when the antecedent is false. If A is false, then A → B is automatically true regardless of B. The same reasoning applies to B → C and C → D: they don’t force anything about B, C, or D once A is false. So the only statement that must be true from what's given is that A is false—the premise itself asserts it. The chain of implications does not require B, C, or D to be true. Therefore, the statement that A is false is the one that must hold.