# Math Help - Set Theory Question

1. ## 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?

2. ## Re: Set Theory Question

Yes that is correct.

3. ## 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?

4. ## 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.

5. ## Re: Set Theory Question

Two sets are equal if they contain exactly the same elements and nothing else. It's as simple as that...

6. ## Re: Set Theory Question

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: : $\{1,2,3\}$

$\{1, 2, 3\}=\{3, 2, 1, 3\}=\{3, 1, 2, 3\}=\{1, 2, 2, 3\}$

7. ## 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}.

8. ## Re: Set Theory Question

Hmm, I'm confused again...sorry for my ignorance.

9. ## Re: Set Theory Question

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

10. ## Re: Set Theory Question

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?

11. ## Re: Set Theory Question

Yes, thank you!

12. ## 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}.