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Symmetric relations

  1. May 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Is this relation symmetric?

    The relation in a set of people, "is brother of"


    2. Relevant equations

    aRb , bRa

    3. The attempt at a solution
    The answer is not symmetric. They gave example says that
    paul may be the bother of Anne but Anne is not the brother of paul
    I thought that if A is brother of B then automatically B is brother of A isnt it?
    I think the reason why i can not understand this is problem of English.
    In my country brother indicates both older and younger, is it different in other country?
     
  2. jcsd
  3. May 5, 2009 #2

    Cyosis

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    It does seem like a linguistic problem. Paul is male Anne is female. Paul is the brother of Anne, Anne is the sister of Paul. It has nothing to do with age only with gender. I hope this clears things up.

    A few more clarifications. If the set would have been the set of all males then the relation would have been symmetric.
     
  4. May 5, 2009 #3
    Ohhhhh right why couldnt i think about that. Anne is name of girl indeed..
    Thankyou!
     
  5. May 5, 2009 #4
    an one more question
    {(x,y) l x^2 + y^2 = 9, x belongs to Z}
    I have to find the domain and range here and as x belongs to Z [interger]
    I thought the domain is all the integers. and if x = 5 then y^2 = -16 which gives answer
    y = 4i so range is all the complex numbers. But the answer is
    domain {-3,-2,-1,0,1,2,3}
    range {-3, -2(root2), -(root5), 0 , root5,2 root 2, 3
     
  6. May 5, 2009 #5

    Cyosis

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    It is the equation of a circle with radius 3. You can be pretty sure that they want real values for y and not complex values. Secondly even if we were to allow complex values for y then the range would still not be all the complex numbers. Example: [itex]y=\frac{1}{2} \Rightarrow x=\frac{1}{2}\sqrt{35} \notin \mathbb{Z}[/itex]
     
  7. May 5, 2009 #6
    Right..ahh why couldnt i think about such things before register the replies..
    Thankyou!
     
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