To me they sound like the same thing.
A or B means to be in either the set of A or B. While A and B means being in both A and B, i.e. the set that is the intersection of the sets.
I've had enough.
So what does Either A or B mean? (I've been taking it to mean the inclusive or)
What does A or B mean? (I've been taking this to mean the exclusive or)
I see people using both interchangeably, and it is nothing short of frustrating. Is there a mathematical convention that dictates how to use the above statements and how to interpret their use?
You do realize that every such articles write... "and oh by the way Either... or means the inclusive or, but sometimes it means the exclusive or"
I was just hoping that someone would have a link to a set of guidelines for mathematical writing to which everyone adhered so that I wouldn't have to go crazy every time a definition or theorem was given using the either...or combination
In his Symbolic Logic textbook, Copi points out that there are two words in Latin for or, vel and aut.
The word vel means or the inclusive sense, at least one is true.
The word aut means or the exclusive sense, one is true but not both.
Copi maintains that we get the symbol that we use for or, , from the first letter of vel. Therefore, in logic we use the inclusive meaning.
V Is the exclusive or... these are just definitions... and they're easy. But not all textbooks are written in logic, they're often written in a "slightly" less logical language called english. Sorry, I think I may be coming across as hostile, and it's not my intention.
I donít find you hostile, just frustrated.
In my lifetime I have had to learn three different systems of logical notations. So I more or less understand.
BTW. The notation for the exclusive or is really relatively new.
It appears nowhere in Copiís texts.