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Basic sets question

  1. Jan 9, 2013 #1
    1. The problem statement, all variables and given/known data

    A = {a,b,c} ; B U C = {c,d,e,f} ; (A∩B) U (C∩A) = ?

    2. Relevant equations

    3. The attempt at a solution

    A U B U C = {a,b,c,d,e,f}
    A ∩ {B U C } = {c}

    My answer: {c}
    Last edited: Jan 9, 2013
  2. jcsd
  3. Jan 9, 2013 #2


    Staff: Mentor

    do it in steps:

    - A intersect B = { ... }
    - C intersect A = { ... }

    then union the results

    Oops just saw you don't have B or C so you need to do set relations as you've shown to get B union C in the mix.

    So I think you're right, the answer is { c }
  4. Jan 9, 2013 #3
    Let's just make it on an easy notation where intersection is multiplication and union is sum:
    A\times B+C\times A=A\times(B+C)=A\times\left\{c,d,e,f\right\}=\left\{ c\right\}
  5. Jan 9, 2013 #4
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