Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Subset proof help!

  1. Jan 25, 2010 #1
    I am stuck on a proof question:

    Prove (A∪B)-C ⊆ A∪(B-C)

    If anyone would be able to help me with this proof it would be much appreciated, as I have an exam on this topic tomorrow afternoon!

    Thanks a lot.
     
  2. jcsd
  3. Jan 25, 2010 #2
    In a proof like this (checking if a set is included into another) you typically take one arbitrary element x from the first set, and prove that it also belongs to the second set. (So any element from the first is included in the second, so the first set is a subset of the second.)

    If x is in the first set, then it is either in A or in B (or both), but certainly not in C. Try to figure out each of the two cases (x in A, x in B), and see if, in both cases, x belongs to the second set.

    Hope this helps.
     
  4. Jan 25, 2010 #3
    Thank you that's helped a lot, I think I've managed to prove it now.

    Hopefully I can do it again tomorrow!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook