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Math Help - R U S, reflexive (Proof Method)

  1. #1
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    R U S, reflexive (Proof Method)

    Hello,

    Can someone please help me do a proof by contradiction on this problem?

    Suppose that r and s are reflexive relations on a set A. Prove or Disprove this statement.

    r U s is reflexive

    I'm stuck with proof by contradiction
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  2. #2
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    Quote Originally Posted by l flipboi l View Post
    Suppose that r and s are reflexive relations on a set A. Prove or Disprove this statement.
    If \mathcal{R} is a reflexive relation on set A then \Delta _A  \subseteq \mathcal{R}.
    If \mathcal{S} is any other relation on A then
    \Delta _A  \subseteq \mathcal{R}\cup \mathcal{S} which means the union is reflexive.
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  3. #3
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    Quote Originally Posted by Plato View Post
    If \mathcal{R} is a reflexive relation on set A then \Delta _A  \subseteq \mathcal{R}.
    If \mathcal{S} is any other relation on A then
    \Delta _A  \subseteq \mathcal{R}\cup \mathcal{S} which means the union is reflexive.
    Thanks! is this direct proof?
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  4. #4
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    Quote Originally Posted by l flipboi l View Post
    is this direct proof?
    That proof is about as direct as it ever gets.
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  5. #5
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    Quote Originally Posted by Plato View Post
    That proof is about as direct as it ever gets.
    Thanks! is there a way to show using proof by contradiction?
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  6. #6
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    Quote Originally Posted by l flipboi l View Post
    Thanks! is there a way to show using proof by contradiction?
    Yes, but then we end up using the very idea I gave you in the so called direct proof.
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