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Math Help - Question about Binary relations

  1. #1
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    Question about Binary relations

    I'm working on binary relation questions and I think I'm just confused about what exactly it means to be a binary relation. One of the questions is

    R[A- B] \supseteq R[A] - R[b] and I'm supposed to show that the superset can't be replaced by an equal sign.

    All of the B's should be capitalized.
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  2. #2
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    Quote Originally Posted by abc512 View Post
    I'm working on binary relation questions and I think I'm just confused about what exactly it means to be a binary relation. One of the questions is

    R[A- B] \supseteq R[A] - R[b] and I'm supposed to show that the superset can't be replaced by an equal sign.

    All of the B's should be capitalized.
    Please define terms.
    What are A & B?
    What does R[A] mean?
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  3. #3
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    A and B are sets. R[A] means the binary relation of A.
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  4. #4
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    Are you sure it is not R[A- B] {\color{red}\subseteq} R[A] - R[b]?
    If not then I do not understand the question.
    Because I can give you a counter example to the way you have written it.
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  5. #5
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    Quote Originally Posted by Plato View Post
    Are you sure it is not R[A- B] {\color{red}\subseteq} R[A] - R[b]?
    If not then I do not understand the question.
    Because I can give you a counter example to the way you have written it.
    No, it's definitely the  \supseteq . Another problem I have is
     R[A \cap B] \subseteq R[A] \cap R[b] and to show that  \subseteq can be replaced by =. Would you be able to explain that one better?
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  6. #6
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    Quote Originally Posted by spaceship42 View Post
    No, it's definitely the  \supseteq . Another problem I have is
     R[A \cap B] \subseteq R[A] \cap R[b] and to show that  \subseteq can be replaced by =. Would you be able to explain that one better?
    OK Look at this example. On \{1,2,3,4,5,6,7,8\}
    define R as xRy if and only if x|y (x divides y).
    Now if A=\{2,4,6,8\}~\&~B=\{1,2,3,4\} then R[A\backslash B] \subset R[A]\backslash R[ B ].
    But R[A]\backslash R[ B ] \not\subseteq R[A\backslash B]

    So what am I not understanding about the question?
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