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 Help Needed!

  1. Dec 12, 2013 #1
    1. The problem statement, all variables and given/known data

    Hey guys!

    I am new to this forum but saw the helpful posts on set theory proofs and wondered if I could finally get some help with this problem:

    Suppose A, B, C, and D are sets with A⊆C and B⊆D. If A∩B=Ø then C∩D=Ø.

    This is a biconditional so I have to prove it both ways correct?

    Any help would be greatly appreciated!

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Dec 12, 2013 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Where's the biconditional? I only see an if then, not an if and only if. What work have you done?

    As stated, the conjecture is false. Are you sure you have the sense correct in terms of which sets are subsets of some other set?
  4. Dec 12, 2013 #3
    My mistake, it is an "if then" statement.
  5. Dec 12, 2013 #4

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    As I previously said, the conjecture as written is false. For example, consider sets of fruits. Let A={apple}, B={banana}, C={apple, orange}, and D={banana, orange}. With this, A⊆C, B⊆D, and A∩B=Ø, but C∩D={orange}, which is not the null set.
  6. Dec 12, 2013 #5
    Wow, the example of using fruit really helped clarify it a lot more. Thank you so much!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted