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Math Help - Prove with relational algebra

  1. #1
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    Prove with relational algebra

    If R and S are both reflexive, then RS is reflexive, too. I need to prove this with relational algebra or disprove by giving a counterexample. Any help?
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    Quote Originally Posted by thehollow89 View Post
    If R and S are both reflexive, then RS is reflexive, too. I need to prove this with relational algebra or disprove by giving a counterexample.
    Any reflexive relation on a set contains the diagonal of the cross product of the set with itself. So does it follow that the intersection of two reflective relations must be reflexive?
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    Quote Originally Posted by Plato View Post
    Any reflexive relation on a set contains the diagonal of the cross product of the set with itself. So does it follow that the intersection of two reflective relations must be reflexive?
    Oh I know it's reflexive, but how exactly am I supposed to show that?
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    Quote Originally Posted by thehollow89 View Post
    Oh I know it's reflexive, but how exactly am I supposed to show that?
    Suppose that each of R\;\&\;S is a reflexive relation on A.
    That means \Delta _A  \subseteq R\;\& \;\Delta _A  \subseteq S\; \Rightarrow \;\Delta _A  \subseteq R \cap S.
    That is the whole proof that R \cap S is reflexive.
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  5. #5
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    Quote Originally Posted by Plato View Post
    Suppose that each of R\;\&\;S is a reflexive relation on A.
    That means \Delta _A \subseteq R\;\& \;\Delta _A \subseteq S\; \Rightarrow \;\Delta _A \subseteq R \cap S.
    That is the whole proof that R \cap S is reflexive.
    Oh thanks. I really do assume that proofs are harder than they actually are.
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