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?
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Yes that is correct.
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?
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.
Two sets are equal if they contain exactly the same elements and nothing else. It's as simple as that...
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: :
Last edited by Plato; March 25th 2013 at 03:54 PM.
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}.
Hmm, I'm confused again...sorry for my ignorance.
Oh, so they are all the same really? Since duplicates don't matter?
Originally Posted by rhymin Oh, so they are all the same really? Since duplicates don't matter? Both of these sets has only one element. Sets are determined only by its contents. Can you think of these in those terms?
Yes, thank you!
All 4 are different ways of writing the same set. The most natural way to write this set is {1,2,3}.
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