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Set Theory Proof

  1. Dec 30, 2004 #1
    Hi all

    (i) A- (B-C) = (A-B) U C
    (ii) A - (B U C) = (A-B) - C

    Which one is always right and which is sometimes wrong?

    My solution

    If x is an element of A - (B-C), then x is not contained in B-C. If y is an element of (A-B) U C, then y is at least one of A-B or C. (i) is sometimes wrong, because y can be C.

    If x is an element of A - (B U C), then x is not contained in (B U C). If y is an element of (A - B) - C, then y is not in B or C. Hence this is always correct. IS my solution correct? Also how would you make (i) true always?

    Thanks
     
  2. jcsd
  3. Dec 30, 2004 #2
    Coutrigrad,
    Bravo!
    You are correct and also the way u have done it is perfect!

    -- AI
     
  4. Dec 30, 2004 #3
    thanks a lot!
     
  5. Dec 30, 2004 #4
    why not use venn diagram to check?
     
  6. Jan 1, 2005 #5
    Scan,
    who said not to?

    -- AI
     
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