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Math Help - Reflexive, symmetric, and transitive

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    Member oldguynewstudent's Avatar
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    Reflexive, symmetric, and transitive

    I'm not sure I have these concepts down well enough. The following is a problem from my professor:

    Let S = {1,2,3,4,5}. On P(S) define the relation \rho as follows: A \rhoB iff A \capB = \emptyset. Is \rho reflexive? Is \rho symmetric? Is \rho transitive?

    Since there are elements in P(S) that do not equal \emptyset when intersecting themself then \rho is not reflexive.

    If A \capB is empty then B \capA is empty so \rho is symmetric.

    {1,2} \cap {3,4} is empty. And {3,4} \cap {2,5} is empty. But {1,2} \cap {2,5} = {2}. So \rho is not transitive.

    Is the above correct? If not please explain where I've gone wrong.

    Happy KwanzHanukmas!
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    Quote Originally Posted by oldguynewstudent View Post
    Let S = {1,2,3,4,5}. On P(S) define the relation \rho as follows: A \rhoB iff A \capB = \emptyset. Is \rho reflexive? Is \rho symmetric? Is \rho transitive?

    Since there are elements in P(S) that do not equal \emptyset when intersecting themself then \rho is not reflexive.

    If A \capB is empty then B \capA is empty so \rho is symmetric.

    {1,2} \cap {3,4} is empty. And {3,4} \cap {2,5} is empty. But {1,2} \cap {2,5} = {2}. So \rho is not transitive.
    Yes, they are all correct.
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    Quote Originally Posted by oldguynewstudent View Post
    I'm not sure I have these concepts down well enough. The following is a problem from my professor:

    Let S = {1,2,3,4,5}. On P(S) define the relation \rho as follows: A \rhoB iff A \capB = \emptyset. Is \rho reflexive? Is \rho symmetric? Is \rho transitive?

    Since there are elements in P(S) that do not equal \emptyset when intersecting themself then \rho is not reflexive.

    If A \capB is empty then B \capA is empty so \rho is symmetric.

    {1,2} \cap {3,4} is empty. And {3,4} \cap {2,5} is empty. But {1,2} \cap {2,5} = {2}. So \rho is not transitive.

    Is the above correct? If not please explain where I've gone wrong.

    Happy KwanzHanukmas!
    You left out "reflexive" but that is easy. Is A\cap A empty?
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