Basic Set Theory: power set - TEMP REPLACEMENT

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Sean Gardiner 5 years, 10 months ago

Created this as a copy of Basic Set Theory: power set.

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

x	integer	5
y	integer	7
B	set	set(5,7)
PB	set	Set of 4 items

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xxxxxxxxxx
 
random(2..8)

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Description

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Generated value: `integer`

→ Used by:

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"Unnamed part" - prompt
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"Unnamed part" → "Step 1." - prompt
"Unnamed part" → "Step 1." - Correct answer
"Unnamed part" → "Step 3." - Correct answer

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Ask the student a question, and give any hints about how they should answer this part.

What is the power set of $\simplify{{set(x,y)}}$ ?

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$\simplify{{set(set(),set(x),set(y),set(x,y))}}$

Marks: Distractor Message:
$\simplify{{set()}}, \simplify{{set(x)}}, \simplify{{set(y)}}, \simplify{{set(x,y)}}$

Marks: Distractor Message:
$\simplify{{set(set(x),set(y),set(x,y))}}$

Marks: Distractor Message:
$\simplify{{set(x)}}, \simplify{{set(y)}}, \simplify{{set(x,y)}}$

Marks: Distractor Message:
$\simplify{{set(set(x),set(y))}}$

Marks: Distractor Message:
$\simplify{{set(x)}}, \simplify{{set(y)}}$

Marks: Distractor Message:
$\simplify{{set(x,y,set(x,y))}}$

Marks: Distractor Message:
$\simplify{{x}}, \simplify{{y}}, \simplify{{set(x,y)}}$

Marks: Distractor Message:
$\simplify{{set(x,y)}}$

Marks: Distractor Message:
$\simplify{{set(set(x,y))}}$

Marks: Distractor Message:
$\simplify{{set(set(),x,y,set(x,y))}}$

Marks: Distractor Message:
$\simplify{{set()}},\simplify{{x}},\simplify{{y}},\simplify{{set(x,y)}}$

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Advice

The power set of $\left\{\var{x},\var{y}\right\}$ is

$\left\{\left\{\right\}, \left\{\var{x}\right\},\left\{\var{y}\right\}, \left\{\var{x},\var{y}\right\}\right\}$ .

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: $\left\{\var{x}\right\},\left\{\var{y}\right\}$
the subset length two: $\left\{\var{x},\var{y}\right\}$ .

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

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This question is used in the following exams:

Week 1: Basic Set Theory - V2 by Sean Gardiner in Discrete Mathematics.
Shivendra's copy of Week 1: Basic Set Theory - V2 by Deactivated user in Deactivated user's workspace.
Shaheen's copy of Week 1: Basic Set Theory - V2 by Shaheen Charlwood in Shaheen's workspace.

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Basic Set Theory: power set - TEMP REPLACEMENT

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Taxonomy: mathcentre

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Sean Gardiner 5 years, 10 months ago

Error in variable testing condition

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Generated value: `integer`

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Basic Set Theory: power set - TEMP REPLACEMENT

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Sean Gardiner 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Choose one from a list

Advanced settings

Generated value: `integer`