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Set theory

  1. Nov 8, 2014 #1
    1. The problem statement, all variables and given/known data
    Set A has twice the number of elements as Set B, 1/3 of the elements of Set A are the same as in Set B, the union of A and B is 42, what is the intersection?

    3. The attempt at a solution

    This was one of my exam questions, and I just want to see what the correct answer was. What I tried to do was
    use the inclusion exclusion principle so

    |AUB| = |A| + |B| - (1/3)*|A|
    42 = |A| + 1/2|A| - (1/3)|A|
    42 = (1/6)|A| + (3/6)*|A| - (2/6)*|A|
    42 = (1/3)|A|

    And 42 is the intersection, but that makes absolutely no sense, can anyone show me the correct way to get the answer?
     
  2. jcsd
  3. Nov 8, 2014 #2

    phinds

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    Draw a Venn diagram using Kn in each section (K different for each section). Answer of 12 falls out trivially.
     
  4. Nov 8, 2014 #3

    Ray Vickson

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    $$42 = |A \cup B| = |A| + |B| - |A \cap B| = 2|B| + |B| - (1/3)\underbrace{(2 |B|)}_{|A|} = (3 - 2/3) |B| = (7/3) |B|$$.
     
  5. Nov 8, 2014 #4

    Dick

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    I think if you had added 1+1/2-1/3 correctly you would have had it.
     
  6. Nov 8, 2014 #5
    Wow elementary math mistakes everywhere haha, yea my mistake. I got it now.
     
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