Basic Set Theory: subsets and set equality

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Daniel Mansfield

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7 years, 9 months ago

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Name	Status	Author	Last Modified
Basic Set Theory: subsets and set equality	Ready to use	Daniel Mansfield	10/02/2022 06:14
Patrick's copy of Basic Set Theory: subsets and set equality	draft	Patrick Joyce	19/07/2017 16:29
Simon's copy of Basic Set Theory: subsets and set equality	draft	Simon Thomas	07/03/2019 14:09
Shivendra's copy of Basic Set Theory: subsets and set equality	draft	Deactivated user	04/06/2019 09:46
Subsets and Set equality	draft	Alexander Corner	27/07/2021 14:59
Mengenlehre: Teilmengen und Mengengleichheit	Ready to use	Andreas Vohns	22/10/2020 21:29

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Question statement

Consider the three individual elements $1, 1$ and $2$ . If we consider these elements as a single unordered collection of distinct objects then we call it the set $\left\{1,1,2\right\}$ . Because sets are unordered this is the same as $\left\{2,1,1\right\}$ and because we only collect distinct objects this is also the same as $\left\{1,2\right\}$ .

For example, let $A=\left\{\var{A[0]},\var{A[1]},\var{A[2]},\var{A[3]}\right\}, B=\left\{\var{B[0]},\var{B[1]},\var{B[2]},\var{B[3]},\var{B[4]}\right\}$ and $C=\left\{\var{C[0]},\var{C[1]},\var{C[2]},\var{C[3]},\var{C[4]},\var{C[5]}\right\}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

A	list	[ 1, 1, 2, 4 ]
B	list	[ 1, 4, 1, 1, 1 ]
C	list	[ 4, 4, 1, 2, 1, 1 ]
AB	integer	0
BC	integer	0
CA	integer	1
AsubsetB	integer	0
BsubsetA	integer	1
CsubsetB	integer	0
BsubsetC	integer	1
CsubsetA	integer	1
AsubsetC	integer	1

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xxxxxxxxxx
 
repeat(random(1..4),4)

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Generated value: `list`

[ 1, 1, 2, 4 ]

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If every element of the set $A$ is also an element of the set $B$ then we say that $A$ is a subset of $B$ : $A \subseteq B$ . Which sets are subsets of one another?

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$A \subseteq B$

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$B \subseteq A$

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$C \subseteq B$

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$B \subseteq C$

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$C \subseteq A$

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$A \subseteq C$

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Advice

You can check to see if $A \subset B$ by progressively checking if each element of $A$ is also in $B$ . There are six questions so you will have to do this six times.

The second part of this question builds on the first. You just need to look at your answers and find the sets which contain each other. It is a bit like the 'less than or equal to' relation in the sense that if you have two numbers $x$ and $y$ where $x \leq y$ and $y\leq x$ , then it must be true that $x=y$ .

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This question is used in the following exams:

Set Notation Practice by Lois Rollings in Algebra 1 - Possibilities.
Joshua's copy of Basic Set Theory by Joshua Capel in Joshua's workspace.
Week 1: Basic Set Theory by Daniel Mansfield in Discrete Mathematics.
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.
Test by Kevin Chalmers in Kevin's workspace.
Set Test by Kevin Chalmers in Kevin's workspace.
Sets by Kevin Chalmers in Kevin's workspace.
DTS - entrance test i by Shaheen Charlwood in Shaheen's workspace.
Shaheen's copy of DTS - entrance test i by Shaheen Charlwood in Shaheen's workspace.
Shaheen's copy of Week 1: Basic Set Theory - V2 by Shaheen Charlwood in Shaheen's workspace.
Week 3: Sets I by Peter Chapman in Peter's workspace.

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Daniel Mansfield 7 years, 9 months ago

Daniel Mansfield 7 years, 9 months ago

Daniel Mansfield 7 years, 10 months ago

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Basic Set Theory: subsets and set equality

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, 10 months ago

Error in variable testing condition

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Generated value: list

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Advanced settings

Generated value: `list`