If A → B and B → C, which statement is true?

If A → B and B → C, which statement is true?

• A. A → C
• B. B → A
• C. C → B
• D. A and B

Answer: (A)

Transitivity of implication is at work here: if A implies B and B implies C, then A must imply C. Here's why: whenever A is true, B is true due to A → B. And whenever B is true, C is true due to B → C. So whenever A is true, C is true, which means A → C holds in all cases. The other possibilities aren’t guaranteed by the given chain. B → A would require the reverse direction, which isn’t provided. C → B would require C to guarantee B, which also isn’t given. And A ∧ B isn’t necessarily true just from A → B and B → C, since A could be false, making A → B vacuously true but not ensuring A ∧ B.

Transitivity of implication is at work here: if A implies B and B implies C, then A must imply C. Here's why: whenever A is true, B is true due to A → B. And whenever B is true, C is true due to B → C. So whenever A is true, C is true, which means A → C holds in all cases.

The other possibilities aren’t guaranteed by the given chain. B → A would require the reverse direction, which isn’t provided. C → B would require C to guarantee B, which also isn’t given. And A ∧ B isn’t necessarily true just from A → B and B → C, since A could be false, making A → B vacuously true but not ensuring A ∧ B.