- #1
kathrynag
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Homework Statement
I need to decide whether the theorem is correct and decide where the proof fails.
AunionB=AunionC, B=C
Homework Equations
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.