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    Reflexive, Symmetric, Boolean

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    1. Determine if the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive where (x,y) R if and only if x = 1.
    a. reflexive
    b. symmetric
    c. antisymmetric
    d. transitive

    2. Find the Boolean product of the two matrices:
    [ 0 1 0 ] [ 0 1 0 ]
    [ 1 1 1 ] [ 0 1 1 ]
    [ 1 0 0 ] [ 1 1 1 ]

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    https://brainmass.com/math/boolean-algebra/reflexive-symmetric-transitive-boolean-products-528755

    Solution Preview

    1.
    a. Reflexive means (x,x) E R for all real number x. However, (2,2) is not E R since the first coordinate 2 is not = 1. R is not reflexive.

    b. Symmetry means (x,y) E R implies (y,x) E R. However, (1,2) E R but (2,1) is not E R is not symmetric.

    c. Antisymmetric means (x,y) E R and x is not = y ...

    Solution Summary

    This solution defines what it means if a product is said to be reflexive, symmetric/antisymmetric, transitive or Boolean. It then shows how to find if a given relation is reflexive, symmetric, antisymmetric, or transitive and explains the logic behind the answer, then shows how to find the Boolean product of two matrices.

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