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!
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.