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Math Help - Very basic contrapositive/converse question

  1. #1
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    Very basic contrapositive/converse question

    I just have a quick question that should be quite easy and basic regarding contrapositives/converses of statements.

    If your professor were to say to you: "If you get at least a B on the final, then you will pass the class,"
    it seems to me a couple things could happen:

    1) If you did NOT get at least a B on the final, I can't automatically assume you did not pass (you did extra credit)
    2) if you passed the class, I can't automatically assume you got at least a B on the final (you did extra credit)

    Am I correct to conclude these statements?

    I realize that if your professor told you "If and only if you get at least a B, then you will pass," then I'd be able to conclude that:
    3) if you didn't get at least a B, you could not have passed
    4) If you did pass the class, you had to have gotten a B.

    I just don't know whether I should assume the same if the "and only if" is not included originally.

    Thanks in advance for any help!
    Chris
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  2. #2
    MHF Contributor
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    Re: Very basic contrapositive/converse question

    I agree with your reasoning. Strictly speaking, the original claim does not mean that getting at least a B is equivalent to passing; it only says that the former implies the latter.
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