Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Possible Duplicate:
Subsets and equality

Hello I'm new to set theory and I want to know how I can solve the following question

Let $U$ be a universe and $A,B$ and $C$ be subsets of $U$. Prove or disprove:

$$(A \cup B) = (A \cup C)\implies B = C$$

(question also found here)

I'm looking at the "Typical element" Method of proving this statement but I'm confused on how to go about it or if it is even the correct method to be using.

share|cite|improve this question

marked as duplicate by Gerry Myerson, Martin Sleziak, Thomas, MJD, Norbert Oct 8 '12 at 18:14

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

ok that makes much more sense to me now! so its saying if B and C are subsets of A then B = C – Daniel D C Oct 8 '12 at 12:27
No! It says nothing about $B$ and $C$ being subsets of $A$. There are no subset symbols in it whatsoever. – Gerry Myerson Oct 8 '12 at 12:28
so i need to give a proof to state that is true – Daniel D C Oct 8 '12 at 12:28
Daniel, look at the answer that has been posted. If you prove it's true, you will single-handedly destroy mathematics! – Gerry Myerson Oct 8 '12 at 12:29
oh yeah whoops :| its been a long night – Daniel D C Oct 8 '12 at 12:29
up vote 2 down vote accepted

Take $A=\{1,2 \}$, $B=\{1 \}$, $C=\{2 \}$. No relation between $B$, $C$.

share|cite|improve this answer
i think im more after this kind of answer – Daniel D C Oct 8 '12 at 12:33
In that link, they are trying to prove something. When you want to disprove something you have to find a counterexample. – PAD Oct 8 '12 at 12:40
no worries thanks for your help – Daniel D C Oct 8 '12 at 12:46

Not the answer you're looking for? Browse other questions tagged or ask your own question.