Simon's copy of Basic Set Theory: set operations

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S Kapur

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4 years, 9 months ago

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S Kapur 4 years, 9 months ago

Gave some feedback: Ready to use

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Simon Thomas 6 years, 1 month ago

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

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, 7, 7, 9 ]
listB	list	[ 3, 4, 2, 3 ]
A	set	set(5,7,9)
B	set	set(3,4,2,9,7)
listN	list	[ 9, 7 ]

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Name

Data type

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, 7, 7, 9 ]

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Advice

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

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

We can think of this as the elements: in $A$ OR in $B$ OR in Both

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

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

We can think of this as the elements: in $A$ AND in $B$

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

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

We can think of this as the elements: in $A$ but NOT in $B$

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

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

We can think of this as the elements: in $B$ but NOT in $A$

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

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

We can think of this as the elements: in $A$ OR in $B$ but NOT in Both.

Give a worked solution to the whole question.

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This question is used in the following exams:

Basic Set Theory by Simon Thomas in Maths support.
SK Exam 1 by S Kapur in S's workspace.
Quiz on Sets by S Kapur in S's workspace.

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Simon's copy of Basic Set Theory: set operations

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S Kapur 4 years, 9 months ago

Simon Thomas 6 years, 1 month ago

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Simon's copy of Basic Set Theory: set operations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

S Kapur 4 years, 9 months ago

Simon Thomas 6 years, 1 month 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`