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Proving a subset

  1. Oct 25, 2011 #1
    1. The problem statement, all variables and given/known data
    The problem I have been given is to prove (A - B) U C is than less or equal to (A U B U C) - (A n B)

    3. The attempt at a solution
    I've tried starting off with just (A-B) U C. Then I would say how x ε c or x ε (A - B). Also if x ε a, then x ε c and x is not in b. If x ε c, since c is a subset of (A U B U C) , x ε (A U B U C). I don't know if this is right or where to go from here.
  2. jcsd
  3. Oct 25, 2011 #2


    Staff: Mentor

    This is a statement about sets, so the relationship is [itex]\subseteq[/itex], not ≤.
    Try to be more careful with the names of the sets, which are A, B, and C, not a, b, and c.
  4. Oct 25, 2011 #3
    i'd say that u can use:

    AUBUC= lAl + lBl + lCl - lBnCl - lAnBl - lAnCl+lAnBnCl

    but i'm not 100% positive just trying to give some help :)
  5. Oct 25, 2011 #4
    My professor said we can also try to prove or find a counterexample to this statement. Let A, B and C be sets. Then (A-B) U C = (A U B U C) - (A n B). I'm not really sure what she means by counterexample.
  6. Oct 25, 2011 #5


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    Science Advisor

    Not only does that not help, it makes no sense. The left side is a set, the right side is a number.

    Even if you meant |AUBUC| that is irrelevant to the problem. Showing that two sets have the same size does not prove they are the same set.
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