If X implies Y and Y implies Z, which deduction is valid?

If X implies Y and Y implies Z, which deduction is valid?

• A. If Y is true, X is true
• B. If Z is true, Y is true
• C. If X is true, Y is true
• D. If X is true, Z is true

Answer: (D)

Chaining implications shows how one condition leads to another. If X implies Y and Y implies Z, then whenever X happens, Y must happen, and when Y happens, Z must happen. Putting those together, X being true forces Z to be true. So the valid deduction is that X implies Z. The other ideas would flip the direction of the implications or merely restate the first rule, so they don’t capture the full link from X to Z that comes from combining both given implications.

Chaining implications shows how one condition leads to another. If X implies Y and Y implies Z, then whenever X happens, Y must happen, and when Y happens, Z must happen. Putting those together, X being true forces Z to be true. So the valid deduction is that X implies Z.

The other ideas would flip the direction of the implications or merely restate the first rule, so they don’t capture the full link from X to Z that comes from combining both given implications.