1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Set theory proof

  1. Apr 20, 2016 #1
    1. The problem statement, all variables and given/known data
    Assume {B, C, D} is a partition of the universal set U, A is a subset of U and A is not a subset of B complement, A is not a subset of C complement, A is not a subset of D complement. Prove that {A ∩ B, A ∩ C, A ∩ D} is a partition of A.

    2. Relevant equations

    3. The attempt at a solution
    I know that this is right intuitively. I know how explain it with words, but I don't know how mathematically.

    A is not a subset of B complement, A is not a subset of C complement, A is not a subset of D complement implies that A has to be distributed among the three subsets. There is nothing left of A because B,C and D is a partition of the universal set. Therefore, the union of the pieces in which A overlaps with B,C,D is A. This pieces are going to be disjoint. Mathematically, I can prove that

    (AnB)n(AnC)n(AnD)=An(BnCnD)= An empty set =empty set
  2. jcsd
  3. Apr 20, 2016 #2


    User Avatar
    Gold Member

    You must prove that the intersection of every two pairs of your new family ##\{A\cap B, A\cap C, A\cap D\}## is empty (using the fact that ##\{B,C,D\}## is a partition of ##U## and that in fact ##A## is not contained in the complement of every set of the partition (that is the same that ##A## has intersection noempty with every set in the partition...)) and that the union of all is ##A##. You will use the distributive law for intersection and union ...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted