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?
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.