If A implies B and B implies C, which statement must be true?

If A implies B and B implies C, which statement must be true?

• A. C implies A
• B. A implies B
• C. A implies C
• D. B implies A

Answer: (C)

When one statement leads to another, and that second one leads to a third, you can chain them to see what must happen overall. If A makes B true, and B makes C true, then A being true guarantees C being true. In other words, A implies C must hold. This is simply the transitive way implications work: the effect of A passes through B to produce C. To see why the other directions aren’t guaranteed, reversing the arrows would require information not given. So the only conclusion that must follow from both premises is that A implies C.

When one statement leads to another, and that second one leads to a third, you can chain them to see what must happen overall. If A makes B true, and B makes C true, then A being true guarantees C being true. In other words, A implies C must hold. This is simply the transitive way implications work: the effect of A passes through B to produce C.

To see why the other directions aren’t guaranteed, reversing the arrows would require information not given. So the only conclusion that must follow from both premises is that A implies C.