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Union/Intersection Proof

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Suppose f: A → B and that E,F are subsets of A.
    Prove the following:
    a) [itex] f(E \cup F) \equiv f(E) \cup f(F) [/itex]
    b) [itex] f(E \cap F) \subset f(E)\cap f(F) [/itex]



    2. Relevant equations

    3. The attempt at a solution
    So far I have solved the first one, but I am having trouble with the second. I have no idea where to begin.

    BiP
     
    Last edited: Mar 17, 2012
  2. jcsd
  3. Mar 17, 2012 #2
    I don't believe b) is true..
     
  4. Mar 17, 2012 #3
    Woops! Sorry I wrote it wrong. I'll change that.

    BiP
     
  5. Mar 17, 2012 #4
    Ok ya that should just be a straight element proof then, just follow your nose, if b is in f(E∩F) then there exists an a in E∩F such f(a)=b, if a is in E∩F then a is in E and F.. and so on and so forth.
     
  6. Mar 17, 2012 #5
    What does "and so on and so forth" supposed to mean? I don't understand your proof sorry. It's incomplete.

    BiP
     
  7. Mar 17, 2012 #6

    micromass

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    Yes, because you are supposed to finish it.
     
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