I was given a problem where I was to find two disjoint partitions, [tex]S_1[/tex] and [tex]S_2[/tex] and a set A such that |A| = 4 and [tex]|S_1| = 3[/tex] and [tex]|S_2| = 3[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

Now the set I was using and the book eventually used was A = {1,2,3,4} and [tex]S_1 = [/tex]{{1},{2},{3,4}} and [tex]S_2 = [/tex]{{1,2},{3},{4}}.

The question I have is probably a few definition questions that the book just doesn't seem to be clear about. Do the S's have to be a collection of sets and not simply a set of numbers? For example, is [tex]S_1 =[/tex] {1,2,3} not a correct partition?

Also, the text asks for "disjoint" partitions, which I assume means [tex]S_1[/tex] and [tex]S_2[/tex] don't share any elements. However, isn't this part of the definition of a partition? That is, any two sets don't share any elements?

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# Homework Help: Partition sets

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