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Set Proof Problems

  1. Oct 15, 2016 #1
    1. The problem statement, all variables and given/known data
    Can anyone please help me solve these questions?



    (1) Prove that (A-B) - (B-C) = A-B



    (2)Simplify (A-( A N B)) N (B-(ANB))



    (3) Simplify ( ( A N ( B U C)) N ( A-B)) N ( B U C')



    (4)Use element property and algebraic argument to derive the property



    (A-B) U (B-C) = (A U B) - (B N C)



    (5) Derive the set identity A U (A NB) = A



    (6) Derive the set identity A N ( A U B) = A



    N stands for intersection.



    Thank you for your time.



    2. Relevant equations
    A-B = A N B'- Set Difference rules
    A N ( A U B) - Distributive rule : (A N A) U (A N B)
    (A' N B') = (A U B)' - De Morgans Law

    3. The attempt at a solution
    Distributive
    rules A N (A U B) = ( A N A) U ( A N B) = A U (A NB) then I dont know how to go there, if i continue with associative rule I simply revert back to the initial step? Same for question 5. For Q 1 (A N B') N ( B' N C) and then I don't know how to go from there.
    Q 2 and 3 got me confused with all the brackets to be honest...I don't even know which rules to use? Any hint???
     
    Last edited: Oct 15, 2016
  2. jcsd
  3. Oct 15, 2016 #2

    PeroK

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    Have you ever seen the following definition that two sets are equal:

    Sets ##A## and ##B## are equal if ##x \in A \iff \ x \in B##
     
  4. Oct 15, 2016 #3
    I actually managed to get the answer to Q 5 and 6
    Q 5 First we state that for all subset of B of the universal set, U U B = U and then we intersect both sides by A.
    Q 6 We state that for all subset if B of the universal set, Null set = Null Set intersect B and then take union of both sides with A.
    It was quite easy, I was quite dumb for not noticing before and now for the other questions...
     
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