Power set - empty set and |P(P(P(S))| - Numbas at mathcentre.ac.uk

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Lois Rollings

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Lois Rollings 7 years, 5 months ago

Created this as a copy of Basic Set Theory: fun and games with the power set.

Name	Status	Author	Last Modified
Basic Set Theory: fun and games with the power set	Ready to use	Daniel Mansfield	02/06/2019 06:57
Power set - empty set and \|P(P(P(S))\|	draft	Lois Rollings	13/08/2020 09:32
Simon's copy of Basic Set Theory: fun and games with the power set	draft	Simon Thomas	07/03/2019 14:23

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Question statement

$\mathcal{P}(A)$ represents the power set of A.

Note that you input sets in the form set(a,b,c,d) and the empty set is input as set().

Give any introductory information the student needs.

			Name	Type	Generated Value

n	integer	0
powern	number	1
powerpn	decimal	dec("2")
powerppn	decimal	dec("4")
p		Definition of variable `p` is empty.

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0..2)

JME function reference

Description

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

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Generated value: `integer`

→ Used by:

powern

This variable doesn't seem to be used anywhere.

Advice

a) Using the fact $P(\left\{\right\}) = 2^{\left|\left\{\right\}\right|} = 2^0 = 1$ . So $P(\left\{\right\})$ is a one-element set which contains $\left\{\right\}$ . There is only one possible answer

$\left\{\left\{\right\}\right\}$ .

b) Rcall that if $|A|$ =n $, then$ |\mathcal{P}(A)|=2^n$.

c) We construct the answer gradually. Since $\left|S\right| = \var{n}$

$\left|\mathcal{P}(S)\right| = 2^\var{n}= \var{powern}$
$\left|\mathcal{P}(\mathcal{P}(S))\right| = 2^{\left|\mathcal{P}(S)\right|} = 2^{\var{powern}}=\var{powerpn}$
$\left|\mathcal{P}(\mathcal{P}(\mathcal{P}(S))\right| = 2^{\left|\mathcal{P}(\mathcal{P}(S))\right|} = 2^{\var{powerpn}}=\var{powerppn}$ .

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Power set - empty set and |P(P(P(S))|

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Lois Rollings 7 years, 5 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Mathematical expression

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Checking accuracy

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Error

Power set - empty set and |P(P(P(S))|

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Lois Rollings 7 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`