If A implies B and B implies C, what can be concluded about A and C?

If A implies B and B implies C, what can be concluded about A and C?

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

Answer: (A)

Transitivity of implication. If A leads to B and B leads to C, then A leads to C. The idea is straightforward: whenever A is true, B must be true; and whenever B is true, C must be true. Put together, whenever A is true, C must be true as well. For a simple example, if being a weekday guarantees the office is open, and the office being open guarantees you can attend a meeting, then being a weekday guarantees you can attend a meeting. This chain doesn’t allow you to conclude anything about C implying A or about B implying A unless additional information is provided. The guaranteed conclusion from the given links is that A implies C.

Transitivity of implication. If A leads to B and B leads to C, then A leads to C. The idea is straightforward: whenever A is true, B must be true; and whenever B is true, C must be true. Put together, whenever A is true, C must be true as well. For a simple example, if being a weekday guarantees the office is open, and the office being open guarantees you can attend a meeting, then being a weekday guarantees you can attend a meeting. This chain doesn’t allow you to conclude anything about C implying A or about B implying A unless additional information is provided. The guaranteed conclusion from the given links is that A implies C.