Given the sentence: "You can access the internet only if you are a computer science major or you are not a freshman" and functions:

  1. a = you can access the internet
  2. b = you are a computer science major
  3. c = you are a freshman

we need to translate into a logical proposition.

My intuitive approach is to say (b v ~c) -> a.

However, the solution suggested is a -> (b v ~c).

Are these two equivalent in the sense that the proposition was really an iff statement? If this is the case, why wasn't it translated to [a -> (b v ~c)] ^ [(b v ~c) -> a]?

  • $\begingroup$ manthanomen and Brian's answers explain the suggested solution well, but I think this interpretation of "only if" may be specific to mathematicians and logicians. In the context of ordinary speech the bi-implication would also be a reasonable interpretation, I think. $\endgroup$ – Trevor Wilson Oct 1 '13 at 2:25

They are not equivalent. Yours is the converse of the desired statement. Translated into English, yours says:

If you are a computer science major or you are not a freshman, then you can access the internet.

Suppose that every student can access the internet; the statement in grey is still true — misleading, perhaps, but true. Your statement just lists two groups of people who can access the internet; it doesn’t say that these are the only groups who can do so.

The original statement, however, would not be true in this situation (assuming that there are some freshmen or some students not majoring in computer science): it says that the only people who can access the internet are comp. sci. majors and non-freshmen. And contrary to what you might at first think, it does not say that all comp. sci. majors and non-freshman can access the internet: it just says that if you’re not a comp. sci. major or a non-freshman, you definitely cannot access the internet.

  • $\begingroup$ Thank you. I need to reconsider my entire life at this point. $\endgroup$ – Rire1979 Oct 1 '13 at 2:25
  • $\begingroup$ @Rire1979: You’re welcome. $\endgroup$ – Brian M. Scott Oct 1 '13 at 2:25

The proposition isn't an iff statement. It's equivalent to saying "If you can access the internet, then you're a computer science major or you're not a freshmen." But there may be computer science majors and non-freshman who still can't access the internet.


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