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Math Help - Help with a Relation

  1. #1
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    Help with a Relation

    Consider the relation R on {1,2,3,4,5} given by xRy \longleftrightarrow x + y >5

    How do I make the matrix for this relation?


    Is the relation transitive? Why?
    Last edited by minkyboodle; October 12th 2009 at 05:16 PM.
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  2. #2
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    Quote Originally Posted by minkyboodle View Post
    Consider the relation R on {1,2,3,4,5} given by xRy \longleftrightarrow x + y >5

    How do I make the matrix for this relation?


    Is the relation transitive? Why?
    I suppose the matrix for the relation would be defined as:

    A = (a_{ij}); \ a_{ij} = \begin{cases} 1 & i+j \geq 5 \\ 0 & i+j < 5 \end{cases}

    The relation is transitive if for any x,y,z \in \{1,2,3,4,5\} : x+y \geq 5 , y+z \geq 5 \Rightarrow x+z \geq 5

    But what happens if you take x=1, y=5, z=2? Is x+z \geq 5?
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