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Let A and B be relations on the set C = {1,2,3,4,5,6}

  1. Nov 15, 2011 #1
    1. The problem statement, all variables and given/known data
    Let A and B be relations on the set C = {1,2,3,4,5,6}. Prove or disprove the following:

    If A and B are symmetric, then A U B is symmetric.


    2. Relevant equations



    3. The attempt at a solution
    The main problem is that I don't know how A U B is defined.

    In general, a relation R is a subset of A x B. For example, {(1,1), (1,2)} is one relation. (ie. I can write 1 R 1, and 1 R 2.)

    Symmetric means that for all x, y in C, if x R y then y R x.

    I know A U B would be read "A or B", but I don't understand it? Is it like (x A y) or (x B y)?

    Then I don't get what A U B would look like if it was symmetric.

    Then to prove it you suppose that if x A y then y A x. You also suppose that if x B y then y B x.

    From here I don't know what I'm supposed to show...
     
  2. jcsd
  3. Nov 15, 2011 #2

    Dick

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    Re: Relations

    AUB means the union of the sets A and B. It's the union of the set of all of the ordered pairs defining the A relation with all of the ordered pairs defining the B relation. If x AUB y, then either x A y or x B y. Does that help?
     
    Last edited: Nov 15, 2011
  4. Nov 15, 2011 #3
    Re: Relations

    So would it be:

    x RUS y if (x R y or x S y) ?

    And the condition for symmetry is if x RUS y then y RUS x?
     
  5. Nov 15, 2011 #4

    Dick

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    Re: Relations

    Exactly.
     
  6. Nov 15, 2011 #5
    Re: Relations

    Perfect, thanks!
     
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