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Suppose that A\B is disjoint from C and x εA.prove that if xεC then xε

  1. Aug 24, 2013 #1
    Suppose that A\B is disjoint from C and x εA.prove that if xεC then xεB
     
  2. jcsd
  3. Aug 24, 2013 #2
    Given A\B is disjoint from C.
    i.e, A\B[itex]\cap[/itex]C=null set.
    But A\B[itex]\cap[/itex]C=(B[itex]\cap[/itex]C)\A
    ∴(B[itex]\cap[/itex]C)\A=null set.
    Which means (B[itex]\cap[/itex]C)=A
    Since x[itex]\in[/itex]A, x[itex]\in[/itex](B[itex]\cap[/itex]C)
    Hence if x[itex]\in[/itex]C, then x[itex]\in[/itex]B
     
  4. Aug 24, 2013 #3

    verty

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    Homework Helper

    Proof by contrapositive works here, very well in fact.
     
  5. Aug 25, 2013 #4

    mfb

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    2017 Award

    Staff: Mentor

    This is not an acceptable way to ask for help at homework problems. In addition, it is in the wrong forum.
     
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