If A implies B and B implies C, which statement is logically equivalent?

If A implies B and B implies C, which statement is logically equivalent?

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

Answer: (C)

The main idea here is the transitive nature of implication: if A leads to B and B leads to C, then A must lead to C. Reason this through step by step: if A is true, then B must be true because A implies B. If B is true, then C must be true because B implies C. Combining those, whenever A is true, C is also true, so A implies C holds. If A is false, the statement A implies C is still true by default. So A implies C is guaranteed by the two given implications. The other options don’t capture this combined consequence. Repeating A implies B or B implies C just restates one link and doesn’t express the direct connection from A to C. The reverse direction, C implies A, goes in the opposite direction and isn’t supported by the chain.

The main idea here is the transitive nature of implication: if A leads to B and B leads to C, then A must lead to C.

Reason this through step by step: if A is true, then B must be true because A implies B. If B is true, then C must be true because B implies C. Combining those, whenever A is true, C is also true, so A implies C holds. If A is false, the statement A implies C is still true by default. So A implies C is guaranteed by the two given implications.

The other options don’t capture this combined consequence. Repeating A implies B or B implies C just restates one link and doesn’t express the direct connection from A to C. The reverse direction, C implies A, goes in the opposite direction and isn’t supported by the chain.