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DISCRETE: A-ø=? (A is defined)

  1. Feb 4, 2014 #1
    1. The problem statement, all variables and given/known data
    Suppose A={ø,1,2,{1,2},{3}}. Determine if each statement is true or false. Give a brief justification for your answers.
    (I finished the majority of them except for the last two)
    g) A-ø=A
    h) A-ø={1,2,{1,2},{3}}

    2. Relevant equations
    The definition of difference between two sets.
    Let A and B both be sets. Then A-B={x: x[itex]\in[/itex]A and x[itex]\notin[/itex]B}

    3. The attempt at a solution
    So basically one of the questions is false and the other is true. Immediately I want to say (h) is true just because A has an empty set in it but after thinking about it I think (g) is true.
    This is because we are trying compare what is in the empty set that A also contains... but the empty set has nothing in it so there is nothing to take from A. Therefore A-ø=A. Is this right? If it's not can someone explain to me why?
    I'm getting quite conflicted as to which one I believe is true. Help understanding which is true would be greatly appreciated. :)
     
  2. jcsd
  3. Feb 4, 2014 #2

    Dick

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    Think about the difference between A-ø and A-{ø}. ø (which has no elements) and {ø} (which has one element ø) are two different things. That might help.
     
    Last edited: Feb 4, 2014
  4. Feb 4, 2014 #3
    Thanks, so (g) is true and (h) is false. If (h) were to be true then it would be A-{emptyset}={1,2,{1,2},{3}}?
     
  5. Feb 4, 2014 #4

    Dick

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    Yes, A-{ø}={1,2,{1,2},{3}}. A-ø=A. You were right.
     
  6. Feb 4, 2014 #5
    Thank you so much :)
     
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