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Set Partitions : Coarseness and Fineness

The meet of the partitions f1,...,fI is the finest partition that is coarser then each fi. The join of the partitions f1,...,fI is the coarsest partition that is finer than each fi. The meet of partitions is denoted and the join of partitions is denoted
I I
&#923; fi (meet) V fi (join)
i = 1 i = 1

(a) If f1,...,fI represent the information of the different traders, what do the meet and join represent?

(b) For:
f1 = { {&#969;1},{ &#969;2, &#969;3, &#969;4},{ &#969;5, &#969;6, &#969;7} }
f2 = { {&#969;1, &#969;2, &#969;3},{&#969;4},{ &#969;5, &#969;6,},{&#969;7} }
compute the meet f1 &#923; f2.

Solution Preview

The answers are written along with the questions, and explained in the attached Word file.

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The meet of the partitions f1,...,fI is the finest partition that is coarser then each fi. The join of the partitions f1,...,fI is the coarsest partition that is finer than each fi. The meet of partitions is denoted and the join of partitions is denoted
I I
&#923; fi (meet) V fi (join)
i = 1 i = 1

(a) If f1,...,fI represent the ...

Solution Summary

Coarseness and finess of partitions is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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