(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to decide whether the theorem is correct and decide where the proof fails.

AunionB=AunionC, B=C

2. Relevant equations

3. The attempt at a solution

We will prove by contradiction. Suppose that A[tex]\cup[/tex]B and A[tex]\cup[/tex]C are not equal. Then there is some object x that is in one and not the other. We proceed by looking at 2 cases:

First look at the case where x[tex]\in[/tex]A[tex]\cup[/tex]B and x[tex]\notin[/tex]A[tex]\cup[/tex]C. Then x[tex]\notin[/tex]A. So x[tex]\in[/tex]B. Also x[tex]\notin[/tex]C. Therefore x is in B and not in C, which contradicts the condition B=C.

I thought the theorme was correct, but I can't find where the proof goes wrong.

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# Homework Help: AunionB=AunionC, B=C

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