Logic

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This is a follow up to a question answered by Dr. Maitzen on December 31 2020.
The statement really was “Only if A, then B”. It came up on a test question that asked the following:
“If A, then B” and “Only if A, then B” are logically equivalent. True or false?
The answer is ‘false’, apparently. I reasoned that “Only if A, then B” is maybe like saying “Necessarily: if A, then B”, and this is clearly different from saying simply “If A, then B”. But I’m not sure. Any chance you might be able to help me see why “If A, then B” and “Only if A, then B” aren’t equivalent? Clearly they say different things, but I’m just not sure how to put my finger on the difference.
I really appreciate the help. Thank you again.
Accepted:December 31, 2020

Accepted:

December 31, 2020