Inclusive OR? Wtf?

[Tea Earl Grey Hot]

I'm studying propositional logic and I learned that "or" means "at least one is true". So you could have "a or b" and even if both a and b were each true then "a or b" is still true. In everyday language however "or" means only one of two things can be true, not both hence the reason we have the phrase "and/or" to mean "at least one is true".

Why not just keep the traditional exclusive meaning of "or" in propositional logic and then have another symbol for "and/or"? Seems simpler to me.

It greatly simplifies things to have two different operators for OR and XOR. Otherwise, the nonexclusive OR would have to be written as " if (a or b) or (a and b)". In my experience, the nonexclusive OR is much more commonly used.

In propositional logic, you actually have to write "(a or b) and not (a and b)" to mean exclusive or. There's no symbol for it.

“(P v Q)” claims that at least one part is true. So “I went to Paris or I went to Quebec” is true just if I went to one or both places. Our “v” symbolizes the inclusive sense of “or”; English also can use “or” in an exclusive sense, which claims that at least one part is true but not both. Both senses of “or” can translate into our symbolism:
• Inclusive “or”: A or B or both = (A v B)
• Exclusive “or”: A or B but not both = ((A v B) · ~(A · B))”

Excerpt From: Harry J. Gensler. “Introduction to Logic: Second Edition.” iBooks. https://itunes.apple.com/WebObjects/MZSt...=495640131