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!

Prove that if A and B are sets, then (A - B) U B = A U B

  1. Oct 19, 2015 #1
    1. The problem statement, all variables and given/known data

    Prove that if A and B are sets, then (A - B) U B = A U B

    I think I might be missing a few steps here.

    2. Relevant equations

    3. The attempt at a solution

    (A - B) U B =

    1. (A ^ ~B) U B =

    2. (A ^ ~B) U (A ^ B) =

    3. A U B
  2. jcsd
  3. Oct 19, 2015 #2
    Hi Leo:

    I think that whether a step is "missing" or not depends on what your teacher expects.
    (W ^ X) U (Y ^ Z) = ((W U Y) ^ (X U Y)) U ((W U Z) ^ (X U Z))
  4. Oct 19, 2015 #3


    User Avatar
    Science Advisor
    Education Advisor

    Issue with step 1 to 2: When I'm in ##B##, but not in ##A##, I'm in set (1) but not in set (2).
    Issue with step 2 to 3: Set (2) is simply equal to ##A##, which may be smaller than set (3).

    I recommend you do not try to "rewrite" the sets, but instead prove two inclusions: First take an arbitrary ##x \in (A - B) \cup B## and argue step by step why it is then in ##A \cup B##. Then take an arbitrary ##x \in A \cup B## and argue why it is in ##(A - B) \cup B##.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Prove that if A and B are sets, then (A - B) U B = A U B