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Homework Help: Prove that if A intersect B = A intersect C then

  1. Oct 11, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that if A [itex]\cap[/itex] B = A [itex]\cap[/itex] C [itex]\Leftrightarrow[/itex] A [itex]\cap[/itex] [itex]\neg[/itex]B = A [itex]\cap[/itex] [itex]\neg[/itex]C

    2. Relevant equations

    3. The attempt at a solution
    I have done a lot of work on this exercise nothing seems to work..
  2. jcsd
  3. Oct 11, 2012 #2
    Can you show us the work you did?
  4. Oct 11, 2012 #3
    All i pretty much did so far was turning the A [itex]\cap[/itex] LB = A [itex]\cap[/itex] C [itex]\Leftrightarrow[/itex] A - B = A - C
    i've tried pretty much everything nothing seems to work
    example : let x E a ---> x E A [itex]\cap[/itex] B ---> x E A [itex]\cap[/itex] C
    yeah i'm pretty much stuck here
    also i tried this one A [itex]\cap[/itex] B = A [itex]\cap[/itex] C [itex]\longrightarrow[/itex] x E A and x E B and x E C [itex]\Longrightarrow[/itex] x E A and x E l B and x E l C And im stuck here.. i need to prove that x E A and x E/ B = x E A and x E/ C...
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