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Thread: n-ary relations and their applications

  1. #1
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    n-ary relations and their applications

    Can anybody do the following problem?
    I don't know how to go about doing it...

    Give an example to show that if R and S are both n-ary relations, then

    $\displaystyle
    P_{i_1,i_2,...,i_m}(R \cap S)$ may be different from $\displaystyle
    P_{i_1,i_2,...,i_m}(R) \cap P_{i_1,i_2,...,i_m}(S) $
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  2. #2
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    Quote Originally Posted by robocop_911 View Post
    Give an example to show that if R and S are both n-ary relations, then$\displaystyle
    P_{i_1,i_2,...,i_m}(R \cap S)$ may be different from $\displaystyle
    P_{i_1,i_2,...,i_m}(R) \cap P_{i_1,i_2,...,i_m}(S) $
    How does your text define $\displaystyle P_{i_1,i_2,...,i_m}(S)$?
    Please be complete in your answer.
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  3. #3
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    Quote Originally Posted by Plato View Post
    How does your text define $\displaystyle P_{i_1,i_2,...,i_m}(S)$?
    Please be complete in your answer.

    The projection $\displaystyle P_{i_1,i_2,...,i_m}$ where $\displaystyle i_1 < i_2 < ... < i_m$, maps the n-tuple $\displaystyle (a_1, a_2,..., a_n) $ to the m-tuple $\displaystyle (a_{i_1}, a_{i_2}, ..., a_{i_m})$, where m <= n.

    In other words, the projection P_i1, i_2,..., i_m deletes $\displaystyle n-m$ of the components of an n-tuple, levaing the i1th, i2th and imth components.
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  4. #4
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    Quote Originally Posted by robocop_911 View Post
    The projection $\displaystyle P_{i_1,i_2,...,i_m}$ where $\displaystyle i_1 < i_2 < ... < i_m$, maps the n-tuple $\displaystyle (a_1, a_2,..., a_n) $ to the m-tuple $\displaystyle (a_{i_1}, a_{i_2}, ..., a_{i_m})$, where m <= n.

    In other words, the projection P_i1, i_2,..., i_m deletes $\displaystyle n-m$ of the components of an n-tuple, levaing the i1th, i2th and imth components.

    For example:
    If $\displaystyle P_{1,3}$ is applied to a 4 tuple (2,3,0,4) gives (2,0)
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