Set Theory Question

• Mar 25th 2013, 03:36 PM
rhymin
Set Theory Question
1) Which of the following sets are equal?
a) {1, 2, 3}
b) {3, 2, 1, 3}
c) {3, 1, 2, 3}
d) {1, 2, 2, 3}

Is this as simple as saying b and c are equal because they contain the same numbers? Or is it more complicated than that?
• Mar 25th 2013, 03:41 PM
Prove It
Re: Set Theory Question
Yes that is correct.
• Mar 25th 2013, 03:42 PM
rhymin
Re: Set Theory Question
Is there anyway to show work for this problem? Or is just saying "b and c are equal because they contain the same set of numbers" enough?
• Mar 25th 2013, 03:43 PM
rhymin
Re: Set Theory Question
Hmm, my friend just told me that they are equal if every element of one is a subset of the other and that they are all equal.

Now I'm more confused lol.
• Mar 25th 2013, 03:44 PM
Prove It
Re: Set Theory Question
Two sets are equal if they contain exactly the same elements and nothing else. It's as simple as that...
• Mar 25th 2013, 03:44 PM
Plato
Re: Set Theory Question
Quote:

Originally Posted by rhymin
1) Which of the following sets are equal?
a) {1, 2, 3}
b) {3, 2, 1, 3}
c) {3, 1, 2, 3}
d) {1, 2, 2, 3}

There is only one set in the list above: : $\{1,2,3\}$

$\{1, 2, 3\}=\{3, 2, 1, 3\}=\{3, 1, 2, 3\}=\{1, 2, 2, 3\}$
• Mar 25th 2013, 03:51 PM
HallsofIvy
Re: Set Theory Question
Plato's point is that a set does not have the same object multiple times. However, some texts would simply ignore the multiple occurances and say that all those sets are the same- and would be better written as just {1, 2, 3}.
• Mar 25th 2013, 03:56 PM
rhymin
Re: Set Theory Question
Hmm, I'm confused again...sorry for my ignorance. :(
• Mar 25th 2013, 03:57 PM
rhymin
Re: Set Theory Question
Oh, so they are all the same really? Since duplicates don't matter?
• Mar 25th 2013, 04:04 PM
Plato
Re: Set Theory Question
Quote:

Originally Posted by rhymin
Oh, so they are all the same really? Since duplicates don't matter?

Both of these sets $\{1\}~\&~\{1,1\}$ has only one element.
Sets are determined only by its contents.
Can you think of these in those terms?
• Mar 25th 2013, 04:07 PM
rhymin
Re: Set Theory Question
Yes, thank you!
• Mar 26th 2013, 03:02 AM
DrSteve
Re: Set Theory Question
All 4 are different ways of writing the same set. The most natural way to write this set is {1,2,3}.