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Math Help - Relation's Proof?

  1. #1
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    Unhappy Relation's Proof?

    A = {1,2,3,4,5,6,7,8,9}
    R=(A1 x A1) U (A2 x A2) U (A3 x A3) U (A4 x A4)


    Proof that R is only Relation that can Partition A like this:

    A = {1,2,3} U {4} U {5,6,7} U {8,9}


    Note that "U" means Union on Sets.

    Please Help me.

    Thank you.
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  2. #2
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    Re: Relation's Proof?

    Quote Originally Posted by reza95 View Post
    A = {1,2,3,4,5,6,7,8,9}
    R=(A1 x A1) U (A2 x A2) U (A3 x A3) U (A4 x A4)

    Proof that R is only Relation that can Partition A like this:

    A = {1,2,3} U {4} U {5,6,7} U {8,9}
    This is an ill-defined question.
    What does "(A1 x A1)" mean?

    Also this is not a homework service. You need to show some effort.
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  3. #3
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    Re: Relation's Proof?

    if u have A1={1,2,3} A2={4} A3={5,6,7} A4={8,9}
    NOW r={A1XA1,A2XA2,A3XA3,A4XA4}
    USE CARTESIAN MULTIPLICATION OF SETS YOU GET
    R={((1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2 ),(3,3))U(4,4)U((5,5),(5,6),(5,7),(6,5),(6,6),(6,7 ),(7,5),(7,6),(7,7))U((8,8),(8,9),(9,8),(9,9))
    NOW TAKE UNION AND U WILL FIND
    R(a,b) has (a,b) belonging to A set
    so A can be partionitioned in above way and the relation is defined
    hence proved
    Thanks from reza95
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