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Set theory problem

  1. Sep 5, 2007 #1
    1. The problem statement, all variables and given/known data

    I have to prove that if A blis a subset of B then B' is a subset of A'.

    2. Relevant equations

    3. The attempt at a solution

    I did:
    Let x belongs to B but x does not belong to A
    =>x does not belong to B' but x belongs to A'
    Hence proved.

    please tell me if I am correct.
  2. jcsd
  3. Sep 5, 2007 #2
    Consider the contrapositive:
    [tex]A \subseteq B \to \left( {x \in A \to x \in B} \right) \to \left( {x \notin B \to x \notin A} \right) \to B' \subseteq A'[/tex]
    Last edited: Sep 5, 2007
  4. Sep 5, 2007 #3


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    How does "x does not belong to B' but does belong to A' " prove B' is a subset of A'?
    For example, if B' were {1, 2, 3, 4, 5} and A' were {5, 6, 7} then x= 6 is not in B' but is in A'. It is certainly not the case that "B' is a subset of A'"!

    To prove "B' is a subset of A'", you must, using the definition, prove "If x is in B' then it is in A'.

    If x is in B', then what can you say about x?
  5. Sep 5, 2007 #4
    You are correct.I was wrong in that arguement.

    Thanks to both of you.
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