Basic Set Theory: power set

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Daniel Mansfield

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7 years, 9 months ago

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Daniel Mansfield 7 years, 9 months ago

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Daniel Mansfield 7 years, 9 months ago

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Name	Status	Author	Last Modified
Basic Set Theory: power set	Ready to use	Daniel Mansfield	29/09/2019 02:45
Power set - list members	draft	Lois Rollings	04/04/2020 15:07
Simon's copy of Basic Set Theory: power set	draft	Simon Thomas	07/03/2019 14:21
Basic Set Theory: power set - TEMP REPLACEMENT	draft	Sean Gardiner	02/06/2019 08:41

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Question statement

The power set of $A$ , written $P(A)$ , is the set of all subsets of $A$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

listB	list	[ 7, 3 ]
PB	set	Set of 4 items
B	set	set(7,3)
b1	integer	7
b2	integer	3

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Name

Data type

Value

xxxxxxxxxx
 
[b1,b2]

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Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `list`

[ 7, 3 ]

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The power set of $\left\{\var{listB[0]},\var{listB[1]}\right\}$ is

$\left\{\left\{\right\}, \left\{\var{listB[0]}\right\},\left\{\var{listB[1]}\right\}, \left\{\var{listB[0]},\var{listB[1]}\right\}\right\}$ .

You can obtain the power set by finding all the subsets of all possible sizes. Since we have a set of size two then the subsets have length at most two. These are

the subset of length zero: $\left\{\right\}$
the subsets of length one: $\left\{\var{listB[0]}\right\},\left\{\var{listB[1]}\right\}$
the subset length two: $\left\{\var{listB[0]},\var{listB[1]}\right\}$ .

Note that the length zero subset is always the empty set, and the largest subset is the set itself.

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Daniel Mansfield 7 years, 9 months ago

Daniel Mansfield 7 years, 9 months ago

Daniel Mansfield 7 years, 9 months ago

Error in variable testing condition

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Generated value: `list`

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Basic Set Theory: power set

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Daniel Mansfield 7 years, 9 months ago

Daniel Mansfield 7 years, 9 months ago

Daniel Mansfield 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `list`