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Math Help - relfexive ,symmetric & transitive

  1. #1
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    relfexive ,symmetric & transitive

    Give an example of a relation that is:
    a) relfexive and symmetric but not transitive
    b) symmetric and transitive but not reflexive
    c)reflexive and transitive but not symmetric
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  2. #2
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    Re: relfexive ,symmetric & transitive

    Quote Originally Posted by franios View Post
    Give an example of a relation that is:
    a) relfexive and symmetric but not transitive
    Reflexive: A has showered with A.
    Symmetric: A has showered with B implies B has showered with A.
    Transitive: A has showered with B and B has showered with C does NOT imply that A has showered with C.
    Last edited by abender; November 13th 2012 at 08:43 AM.
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  3. #3
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    Re: relfexive ,symmetric & transitive

    Quote Originally Posted by franios View Post
    Give an example of a relation that is:
    b) symmetric and transitive but not reflexive
    Reflexive: A is NOT a full sibling to A.
    Symmetric: A is a full sibling to B implies B is a full sibling to A.
    Transitive: A is a full sibling to B and B is a full sibling to C implies that A is a full sibling to C.
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  4. #4
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    Re: relfexive ,symmetric & transitive

    Quote Originally Posted by franios View Post
    Give an example of a relation that is:
    c)reflexive and transitive but not symmetric
    Reflexive: A\leq A.
    Symmetric: A\leq B does NOT imply B\leq A.
    Transitive: A\leq B and B\leq C implies A\leq C.
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