You can legally buy alcohol only if you are at least 21 years old.

laur22 July 26, 2017

Only if

"You can legally buy alcohol only if you are 21." Then the 21 should be the necessary but in the problem I just did it has it as the sufficient even when the answer notes says the opposite?

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Mehran July 28, 2017

@laur22 the correct answer choice here is the contrapositive.

You are correct that "only if" introduces the necessary condition, so the statement would be diagrammed as follows:

LBA ==> at least 21

The contrapositive, which is identical in meaning, is created by reversing and negating the principle as follows:

not at least 21 ==> not LBA

That is why (A) is the correct answer.

Hope that helps! For a more in-depth discussion of these concepts, please watch our video lesson on Sufficient & Necessary conditions.