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How to prove it 3.3 exercise help please

  1. Aug 18, 2013 #1
    I am currently reading vellemans how to prove it for the purpose of being able to construct a proof on my own. I would like to carry on this knowledge to also help me out with spivaks calculus So the problem is:

    Prove that if a and b\c are disjoint, then a[itex]\bigcap[/itex]b[itex]\subseteq[/itex]c.
    1.goal: a[itex]\bigcap[/itex]b\c=∅ → a[itex]\bigcap[/itex]b[itex]\subseteq[/itex]c

    2. Givens:a[itex]\bigcap[/itex]b\c=∅ Goal:a[itex]\bigcap[/itex]b[itex]\subseteq[/itex]c

    3.Givens:a[itex]\bigcap[/itex]b\c=∅ x[itex]\in[/itex]a x[itex]\in[/itex]b Goal: x[itex]\in[/itex]c
    This is as far as I got. I haveE no idea where to go from here and I feel the solution is starting right at me. I think it might have something to do with the fact that a and b\c are disjoints. This might be in the wrong section but I don't no where else to put it
    Last edited: Aug 18, 2013
  2. jcsd
  3. Aug 18, 2013 #2


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    hi eddiep1993! welcome to pf! :smile:
    that's right :smile:

    if x ε a, then x not ε in b/c …

    carry on from there :wink:
  4. Aug 24, 2013 #3


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    Maybe: a[itex]\bigcap[/itex]b\c=∅ x[itex]\in[/itex]a x[itex]\in[/itex]b x[itex]\notin[/itex]c Goal: contradiction
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