Sets: Set notation

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Ruth Hand

said

Ready to use

3 years, 9 months ago

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Christian Lawson-Perfect 2 years, 6 months ago

Published this.

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Ruth Hand 3 years, 9 months ago

Gave some feedback: Ready to use

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Ruth Hand 3 years, 9 months ago

Created this as a copy of Sets: Set logic.

Name	Status	Author	Last Modified
Probability: from a Venn diagram	Ready to use	Ruth Hand	16/01/2023 13:40
Probability: Conditional Probability 1	Ready to use	Ruth Hand	16/01/2023 14:35
Sets: Venn diagram	Ready to use	Ruth Hand	16/01/2023 13:14
Probability: Conditional probability 2 - with Venn	Ready to use	Ruth Hand	16/01/2023 14:22
Sets: Set logic	Ready to use	Ruth Hand	16/01/2023 13:24
Sets: set inequality	Ready to use	Ruth Hand	16/01/2023 13:25
Sets: Set notation	Ready to use	Ruth Hand	16/01/2023 13:25
Probability: Conditional Probability 3 - without Venn	Ready to use	Ruth Hand	16/01/2023 14:20

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

length	list	[ 4, 5 ]
ltv	integer	1
Bltv	range	2..2
w1	integer	12
w2	integer	7
w3	integer	2
W	list	[ 60, 35, 10 ]
m	integer	5
ansb	set	set(2)

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[random(2..6), random(2..6)]

JME function reference

Description

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

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Generated value: `list`

[ 4, 5 ]

This variable doesn't seem to be used anywhere.

List of numbers

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

Given that $W = \{ \var{w1}, \var{w2}, \var{w3}\}$

Find the set
$\{\var{m}w|w \in W\}$

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Correct answer

xxxxxxxxxx
 
W

The list of numbers that the student should enter. The order does not matter.

Allow the student to enter fractions?

Display the correct answers as fractions?

Is the answer a set?

If ticked, the number of times an element occurs doesn't matter, only whether it's included at all.

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Separator

The substring that should separate items in the student's list

Advice

Let us breakdown the set notation

part a)

$\{\var{m}w|w \in W\}$ can be read as "the set of numbers $\var{m} \times w$, for each $w$ in the set $W$".

So to create the new set, we take each element from $W$ and multiply by $\var{m}$.

\[ \begin{split} \{\var{m}w|w \in W\} &= \{\var{m} \times \var{w1}, \var{m} \times \var{w2}, \var{m} \times \var{w3}\} \\ &= \{\var{m*w1}, \var{m*w2}, \var{m*w3}\} \end{split} \]

part b)

$\{x \in \mathbb{N} | \var{ltv} <x \le \var{2*ltv}\}$ is read as "the set of numbers taken from the Natural numbers, given that each number is greater than $\var{ltv}$ but less than or equal to $\var{2*ltv}$":

\[ \{x \in \mathbb{N} | \var{ltv} <x \le \var{2*ltv}\} = \var{ansb} \]

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 3 years, 9 months ago

Ruth Hand 3 years, 9 months ago

Error in variable testing condition

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Generated value: `list`

Parts

List of numbers

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Sets: Set notation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 3 years, 9 months ago

Ruth Hand 3 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

List of numbers

Generated value: `list`