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Math Help - is "or" exclusive?

  1. #1
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    Question is "or" exclusive?

    this one has been bugging me for a while now. we have just finished doing inequalities in class. here is an example of my problem:
    y>-4 AND y<2
    because AND is in there the way you would graph this would be to select all numbers between -4 and 2 because AND means that y has to qualify for BOTH inequalities for the statement to be true.

    here is my problem:
    y>-4 OR y<2
    my math teacher says that in this case when graphing this the answers would be "all real numbers" but doesn't OR mean that it CANNOT qualify for both which means that y could equal any number lessthan -4 or any number greater than 2?

    can someone PLEASE help me with this!?!?!?!
    i love math but i dislike my math teacher to the extreme and would like nothing better than to prove her wrong!!!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by pacman529 View Post
    this one has been bugging me for a while now. we have just finished doing inequalities in class. here is an example of my problem:
    y>-4 AND y<2
    because AND is in there the way you would graph this would be to select all numbers between -4 and 2 because AND means that y has to qualify for BOTH inequalities for the statement to be true.

    here is my problem:
    y>-4 OR y<2
    my math teacher says that in this case when graphing this the answers would be "all real numbers" but doesn't OR mean that it CANNOT qualify for both which means that y could equal any number lessthan -4 or any number greater than 2?

    can someone PLEASE help me with this!?!?!?!
    i love math but i dislike my math teacher to the extreme and would like nothing better than to prove her wrong!!!
    I'm afraid your teacher is correct. The "OR" statement in Mathematics is defined such that if we have the statement "p OR q" the possible outcomes of the statement are:
    p q "p OR q"
    T T T
    T F T
    F T T
    F F F

    The only way to make "y>-4" OR "y<2" false is to find a real number such that y>-4 is false and y<2 is false at the same time. There is no such real number, as you can readily see.

    The problem you are having with the "OR" statement is not uncommon. The way Mathematicians define "OR" is not the same way as the word "or" is used in English. This can cause much confusion!

    -Dan
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  3. #3
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    hey thanks a bunch! (Grrr....)
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by pacman529 View Post
    hey thanks a bunch! (Grrr....)
    Sorry for the bad news. I DO feel your pain!

    -Dan
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