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#1 2007-09-15 14:11:50

MarkusD
Member
Registered: 2006-10-08
Posts: 28

Adding and Subtracting from a Set

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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#2 2007-09-15 16:23:26

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Adding and Subtracting from a Set

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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#3 2007-09-15 16:54:33

MarkusD
Member
Registered: 2006-10-08
Posts: 28

Re: Adding and Subtracting from a Set

Ahh ok. Very clear now smile

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