Should this be conditional or biconditional?

You can access Internet from campus only if you are a CS major or you are not a freshman

How can the above English sentence be translated into a logical expression?

I think this is biconditional but in the book by Kenneth Rosen (7th edition, example 12 on page 11), it is written as conditional.

My solution is the following:

P = You can access Internet. Q = CS major. R = Freshman. So, it should be P <=> (Q + !R)

But in the book it is written as P => (Q + !R)

What seems like the correct answer? I know that conditional is a subset of biconditional. But shouldn't biconditional be the stricter solution?

• Whoever is downvoting, can you please leave a comment on what is wrong with the question? Mar 8, 2016 at 21:50
• "$p$ only if $q$" means "if $p$ then $q$". Mar 8, 2016 at 22:19
• Further, "$p \Leftrightarrow q$" is "$p$ if and only if $q$".$$\begin{array}{ll}p\Leftarrow q & p\textsf{ if }q\\p\Rightarrow q & p\textsf{ only if }q\\p \Leftrightarrow q & p\textsf{ if and only if }q\end{array}$$ Mar 9, 2016 at 3:55

1 Answer

The statement says that you can access internet from campus only if you are a CS major or you are not a freshman. This can be rewritten as an if-then statement: "If you can access the internet then you are a CS major or a freshman". As these are the ONLY ways of being able to access the internet. So if you have access to the net then you must be a CS major or not a freshman, as these are the only two groups of people who are ever allowed on the internet. The statement is not saying that "If you are a CS major or if you are not a freshman then you can access the internet." Being a CS major or not a freshman is a necessary but not a sufficient condition for access to the net. So in conclusion $$P\to (Q \lor \neg R)$$ Is correct. Comment if you need more clarification.

• For example you could be a CS major who hasn't signed the usage agreement contract so you're not allowed to access the net yet. Mar 8, 2016 at 22:03
• got it, thanks :) Mar 8, 2016 at 22:04