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This is from Discrete Mathematics and its Applications enter image description here

This is the book means when mentions a list of common ways to express conditional statements enter image description here

After going through the list, I immediately recognized "q is necessary for p". Translating to the "if p, then q" form, I got "If you want to get promoted, you must wash the boss's car.

Another interpretation of this that I got - from what I learned on Clarifying on how if p,q is logically equivalent to p only if q is

"You can get promoted only if you wash the boss's car". This means the only path to promotion is washing the boss's car. If you managed to get promoted(get there) without washing the car, the contract is broken.

Does all of that sound right?

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committedandroider
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  • You literally asked this question just a few hours ago and marked it as answered: http://math.stackexchange.com/questions/1118530/clarifying-on-how-if-p-q-is-logically-equivalent-to-p-only-if-q/1118554#1118554 – Daniel W. Farlow Jan 25 '15 at 10:09
  • No this is another question - verifying my work on another problem. – committedandroider Jan 25 '15 at 21:24
  • It uses the exact same principle you discussed in your other question. Don't think I've ever seen a duplicate of a duplicate on the same day by the same user. Pretty impressive. – Daniel W. Farlow Jan 25 '15 at 21:39
  • haha but " If those answers do not fully address your question". In this case, I think i meet that requirement because this is an application of the other question. I think it's pretty justified to say, ask a question about the quadratic formula in general and then ask another question or two to make you're doing it right. – committedandroider Jan 25 '15 at 22:04

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Your statement is almost correct. In mathematics "only if" would mean "the only path to promotion includes washing the boss's car". Don't forget that "washing the boss' car" may not be enough to get "a path to promotion".

user21820
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  • so if you don't wash the car, your path does no meet the requirement of going to promotion because it doesn't include washing the car, but it could have other stuff? – committedandroider Jan 25 '15 at 21:29
  • @committedandroider: What your path has is irrelevant for "promotion" once it doesn't have "washing the boss' car". My point is that even if it has "washing the boss' car", it is not necessarily sufficient for "promotion". – user21820 Jan 26 '15 at 07:43