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Math Help - intersecting relationship with set

  1. #1
    Member Jskid's Avatar
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    intersecting relationship with set

    The relation R on Z is defined by (x,y) in R if and only if x-y is even. Write R \cap (\{1,2,3\}x\{1,2,3\}) as a set by listing its elements.

    The \cap confuses me. Is the question asking which elements of the given set are in R? Then that would be (\{1,1\},\{2,2\},\{3,3\},\{1,3\}).
    Last edited by Jskid; October 8th 2011 at 06:03 PM. Reason: currley braces
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  2. #2
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    Re: intersecting relationship with set

    Quote Originally Posted by Jskid View Post
    The relation R on Z is defined by (x,y) in R if and only if x-y is even. Write R \cap (\{1,2,3\}\times\{1,2,3\}) as a set by listing its elements.
    The \cap confuses me. Is the question asking which elements of the given set are in R? Then that would be (\{1,1\},\{2,2\},\{3,3\},\{1,3\}).
    That is the correct idea.
    However, it should be written as \{(1,1),~(2,2),~(3,3),~(1,3),\}.
    Relations are sets of pairs.
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    Re: intersecting relationship with set

    Note the last comma that Plato left as a hint.
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    Member Jskid's Avatar
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    Re: intersecting relationship with set

    Does order matter? For example is (1,3) different than (3,1)?
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    Re: intersecting relationship with set

    Of course the order matters. If you have ever read about unrequited love, you should know.
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    Member Jskid's Avatar
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    Re: intersecting relationship with set

    Quote Originally Posted by emakarov View Post
    Of course the order matters. If you have ever read about unrequited love, you should know.
    I think I misunderstood my prof. Order doesn't matter when {(1,2),(3,4)}={(3,4),(1,2)} right?

    Someone told me parentheses are just for holding things together but how is that different than curly braces?
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    Re: intersecting relationship with set

    order doesn't matter in listing set elements. it DOES matter in listing ordered pairs (note the "ordered" in ordered pair).

    the ordered pair (a,b) is not, in general, the same pair as (b,a).

    for example, if R is the relation <, then (3,4) is in R, but (4,3) is NOT.
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    Re: intersecting relationship with set

    Quote Originally Posted by Jskid View Post
    I think I misunderstood my prof. Order doesn't matter when {(1,2),(3,4)}={(3,4),(1,2)} right?
    Someone told me parentheses are just for holding things together but how is that different than curly braces?
    A relation on a set is subset of the cross product of the set with itself.
    That means that relations are sets of ordered pairs.
    Note the word ordered.
    (1,2)\ne (2,1) but \{1,2\}=\{2,1\}
    So you are correct \{(1,2),(3,4)\}=\{(3,4),(1,2)\}
    BUT \{(1,2),(4,3)\}\ne\{(3,4),(1,2)\}.
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