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Math Help - Either A or B

  1. #1
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    Either A or B

    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?
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  2. #2
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    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.
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  3. #3
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    What?


    For example...

    two numbers a, b satisfy the following

    Either a <= b or b <= a.

    This means that it covers the inclusive case too... since if a <=b and b <= a we have a = b.... so how can it mean the exclusive case?
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  4. #4
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    Quote Originally Posted by Noxide View Post
    What?


    For example...

    two numbers a, b satisfy the following

    Either a <= b or b <= a.

    This means that it covers the inclusive case too... since if a <=b and b <= a we have a = b.... so how can it mean the exclusive case?
    In mathematics the disjunction "or" should be taken to mean that A\text{ or }B is true if and only if A is true and B is false, A is false and B is true, or A and B are true.
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  5. #5
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    Quote Originally Posted by Drexel28 View Post
    In mathematics the disjunction "or" should be taken to mean that A\text{ or }B is true if and only if A is true and B is false, A is false and B is true, or A and B are true.
    When the word either is subsequent to the statement A or B, does anything change?
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  6. #6
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    Quote Originally Posted by Noxide View Post
    When the word either is subsequent to the statement A or B, does anything change?
    A or B and either A or B are the same.
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  7. #7
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    How does one denote the exclusive disjunction with english? Is it common in mathematics to write "... but not both" when the exclusive disjuntion is intended?
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  8. #8
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    Quote Originally Posted by Noxide View Post
    How does one denote the exclusive disjunction with english? Is it common in mathematics to write "... but not both" when the exclusive disjuntion is intended?
    Exclusive or - Wikipedia, the free encyclopedia
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  9. #9
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    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
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  10. #10
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    In English Grammar, not "mathematics", "either A or B" typically means the exclusive or: A or B but not both. I would be very cautious about assuming there is a "one to one relation" between English Grammar and mathematical symbols!
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  11. #11
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    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,  \vee , from the first letter of vel. Therefore, in logic we use the inclusive meaning.
    Last edited by Plato; January 17th 2011 at 08:13 AM.
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  12. #12
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    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.
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  13. #13
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    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 \underline{\vee } for the exclusive or is really relatively new.
    It appears nowhere in Copiís texts.
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