Basic Set Theory: set operations

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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: set operations	Ready to use	Daniel Mansfield	31/05/2019 02:06
Lois's copy of Basic Set Theory: set operations	draft	Lois Rollings	30/09/2017 16:12
Simon's copy of Basic Set Theory: set operations	Ready to use	Simon Thomas	14/07/2020 18:00
William's copy of Basic Set Theory: set operations	draft	William Bean	05/07/2019 12:05
Bewerkingen met verzamelingen kopie nog aan te passen	draft	Johan Maertens	29/07/2020 11:59
Set Operations	draft	Alexander Corner	11/10/2020 16:51
Operationen mit Mengen	Ready to use	Andreas Vohns	23/10/2020 06:01

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Question statement

Consider the sets $A = \var{A}$ and $B = \var{B}$ . Find the union, intsersection and set differences below. Use the NUMBAS syntax set(1,2,3) for $\left\{1,2,3\right\}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

listA	list	[ 5, 6, 8, 8 ]
listB	list	[ 2, 2, 0, 4 ]
A	set	set(5,6,8,7)
B	set	set(2,0,4,5,7)
listN	list	[ 5, 7 ]

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Value

xxxxxxxxxx
 
repeat(random(5..9),4)

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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`

[ 5, 6, 8, 8 ]

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The union of two sets is the set of elements from either set

$A \cup B = \left\{ x\, |\, x \in A \text{ or } x \in B\right\}$

The intersetction of two sets is the set of elements common to both sets

$A \cap B = \left\{ x\, |\, x \in A \text{ and } x \in B\right\}$

The difference $A-B$ is the set of elements from $A$ which are not in $B$ :

$A - B = \left\{ x \in A |\, x \notin B\right\}$

Similarly, the difference $B-A$ is the set of elements from $B$ which are not in $A$ :

$B - A = \left\{ x \in B |\, x \notin A\right\}$

The symmetric difference $A \Delta B$ is the union of the set differences, but it can also be expressed as the union minus the intersection

$A \Delta B = (A \cup B) - (A \cap B)$ .

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This question is used in the following exams:

Homework 1: Practice of Sets by Deirdre Casey in Griffith Foundations of Computing.
Possible questions by Lois Rollings in Algebra 1 - Possibilities.
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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.

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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

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Basic Set Theory: set operations

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`