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Disjoint proof

  1. May 23, 2008 #1
    Hi everyone,

    Could someone please show me how to prove this?

    1. The problem statement, all variables and given/known data

    Determine |A U B| in terms of |A| and |B| assuming that A and B are disjoint

    2. Relevant equations



    3. The attempt at a solution

    I know that A U B must be finite because A and B are disjoint, but besides that I don't know how I would go about proving this.

    Could someone please show me how to?

    Thank you
     
  2. jcsd
  3. May 23, 2008 #2
    There are some intuitive ways to answer this...
    (i) The easiest way is to draw a Venn diagram and see what you think the answer might be
    (ii) Secondly (and more formally) you could formulate the answer in terms of 'indicator functions'

    [tex]i_X(x)= \begin{cases} 0 & \mbox{if }x \notin X \\ 1 & \mbox{if }x \in X [/tex]

    Try the first part and then see if you can do the same via the second
     
  4. May 23, 2008 #3
    Thank you very much

    Regards
     
  5. May 23, 2008 #4

    matt grime

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    Science Advisor
    Homework Helper

    Just because A and B are disjoint, does not in any way imply that AuB is finite. Just count the elements (assuming both A and B are finite).
     
  6. May 24, 2008 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Suppose A= {a}, B= {b}. What is AUB? What is |A|? What is |B|? What is |AUB|?

    Suppose A= {a, b, c}, B= {u, v, w, x, y, z}. What is AUB? What is |A|? What is |B|? What is |AUB|?

    Do those examples give you any ideas? When you have no idea how to do a general problem, look at simple examples.
     
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