www.company.com module code ma1032n: logic lecture for week 6 2012-2013 autumn
TRANSCRIPT
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Module Code MA1032N:Logic
Lecture for Week 6
2012-2013 Autumn
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AgendaWeek 6 Lecture coverage:
– Power Set
– Cartesian Product
– Partitions
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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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Power Set (Cont.)
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Power Set (Cont.)
Example:
So If B = 2 then P(B) = 4 =22
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Power Set (Cont.)
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Power Set (Cont.)
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Power Set (Cont.)
Theorem 2
A set containing n distinct elements has 2n subsets
More formally:
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The Cartesian Product of Two Sets
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The Cartesian Product of Two Sets(Cont.)
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The Cartesian Product of Two Sets(Cont.)
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Partitions
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Partitions (Cont.)
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Set Partition
A
WX Y
In this diagram, the set A (the rectangle) is partitioned into sets W,X, and Y.
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Partitions (Cont.)
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Partitions (Cont.)
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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: