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www.company.com Module Code MA1032N: Logic Lecture for Week 6 2012-2013 Autumn
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www.company.com Agenda Week 6 Lecture coverage: –Power Set –Cartesian Product –Partitions
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www.company.com Power Set The set whose elements consist of all the subsets of a given set A is called the power set of A. This set is written P(A). Thus P(A) = {X:X ⊆ A }
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www.company.com Power Set (Cont.)
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www.company.com Power Set (Cont.) Example: So If B = 2 then P(B) = 4 =2 2
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www.company.com Power Set (Cont.)
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www.company.com Power Set (Cont.)
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www.company.com Power Set (Cont.) Theorem 2 A set containing n distinct elements has 2 n subsets More formally:
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www.company.com The Cartesian Product of Two Sets
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www.company.com The Cartesian Product of Two Sets (Cont.)
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www.company.com The Cartesian Product of Two Sets (Cont.)
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www.company.com Partitions
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www.company.com Partitions (Cont.)
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www.company.com Set Partition In this diagram, the set A (the rectangle) is partitioned into sets W,X, and Y.
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www.company.com Partitions (Cont.)
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www.company.com Partitions (Cont.)
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www.company.com Partitions (Cont.) We implied in our definition of partition that the number of blocks in a partition is finite. A more general definition would allow for an infinite number of blocks, although we will not be concerned with these. However:
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