Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Maybe: a[itex]\bigcap[/itex]b\c=∅ x[itex]\in[/itex]a x[itex]\in[/itex]b x[itex]\notin[/itex]c Goal: contradiction
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook