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Why does the following not hold:
(AUB)\B=A
It would seem that adding something to a set and then taking it away would leave the original set, but my book tells me this doesnt hold.
I was able to prove (AUB)\BCA but am curious why it does not equal A.
Last edited by MarkusD (2007-09-15 14:12:16)
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The thing about sets is that when there are duplicates, you remove all but one. So consider:
A = {1, 2, 3}
B = {1, 2}
Then A U B = {1, 2, 3}
And (A U B) \ B = {1, 2, 3} \ {1, 2} = {3}
Which of course, is not equal to A.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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Ahh ok. Very clear now
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