Lois's copy of set5 - Cartesian Products - Numbas at mathcentre.ac.uk

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Lois Rollings

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Lois Rollings 7 years, 6 months ago

Created this as a copy of set5 - Cartesian Products.

Name	Status	Author	Last Modified
set5 - Cartesian Products	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Blathnaid's copy of set5 - Cartesian Products	draft	Blathnaid Sheridan	27/02/2017 14:38
Lois's copy of set5 - Cartesian Products	draft	Lois Rollings	09/10/2017 15:40
Luis's copy of set5 - Cartesian Products	draft	Luis Hernandez	30/11/2018 17:36
Producto cartesiano de conjuntos	draft	Luis Hernandez	23/01/2019 21:20
Enumerar los elementos de un producto cartesiano ...	Ready to use	Luis Hernandez	14/12/2020 19:22

There are 6 other versions that do you not have access to.

Question statement

Let $A=\var{set1}$ , let $B=\var{set2}$ , let $C=\var{set4}$ and let $D=\var{set5}$ .

List the elements of the following sets.

Input sets in the form set(a,b,c,d) .

For example set(1,2,3) gives the set $\{1,2,3\}$ .

Element $(a,b)$ of a Cartesian product is entered, and represented, as $[a,b]$ .

For example set([1,1],[1,2],[2,3])gives the set $\{[1,1], [1,2], [2,3]\}$ .

The empty set is input as set().

Give any introductory information the student needs.

			Name	Type	Generated Value

			a	integer	3
			b	integer	2

			Name	Type	Generated Value

list1	list	[ 19, 15, 6 ]
list2	list	[ 65, 35 ]
list4	list	[ 15, 19, 23 ]
list5	list	[ 35, 23 ]
list9	list	Nested 4×2 list
list10	list	Nested 4×3 list
list_extra	list	[ 23 ]

			Name	Type	Generated Value

set1	set	set(19,15,6)
set2	set	set(65,35)
set3	set	Set of 6 items
set4	set	set(15,19,23)
set5	set	set(35,23)
set6	set	set([ 35, 19 ],[ 35, 15 ])
set7	set	set(19,15)
set8	set	set(35)
set10	set	Set of 4 items
set11	set	set(6,23)
set12	set	set(65,23)
set14	set	Set of 4 items
set15	set	set([ 19, 35 ],[ 15, 35 ])
set16	set	Set of 3 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..3)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

b
list1
list4

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Part e) Gap-fill
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Part f) Gap-fill
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Gap-fill

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

$A \times B=\;$ Unnamed gap

Advice

a)

$A \times B$ is the set of all pairs $(a,b)$ , where $a \in A$ and $b \in B$ .

b)

$B \cap D$ is the set of all elements present in both $B$ and $D$ , i.e. $\var{set2 and set5}$ .

$A \cap C$ is the set of all elements present in both $A$ and $C$ , i.e. $\var{set1 and set4}$ .

$(B\cap D)\times (A\cap C)$ is the set of pairs of all pairs $(x,y)$ , where $x \in B \cap D$ and $y \in A \cap C$ .

c)

$(A\cap C)\times (A\cap C)\times (C\cap D)$ is the set of all triples $(x,y,z)$ , where $x \in A \cap C$ , $y \in A \cap C$ and $z \in C \cap D$ . Note that $x$ and $y$ do not have to be different.

d)

$A-C$ is the set of all elements present in $A$ but not in $C$ , i.e. $\var{set1-set4}$ .

$C-A$ is the set of all elements present in $C$ but not in $A$ , i.e. $\var{set4-set1}$ .

$(A-C) \cup (C-A)$ is the set of all elements which are either in $A-C$ , or in $C-A$ , so $(A-C) \cup (C-A) = \var{(set1-set4) or (set4-set1)}$ .

e)

$(A \times D)$ is the set of all pairs of elements $(a,d)$ , with $a \in A$ and $d \in D$ , i.e. $\var{set(product(list(set1),list(set5)))}$ .

$C \times B)$ is the set of all pairs of elements $(c,b)$ , with $c \in C$ and $b \in B$ , i.e. $\var{set(product(list(set4),list(set2)))}$ .

$(A \times D) \cap (C \times B)$ is the set of all pairs present in both of the previous sets.

f)

$C \cap D$ is the set of all elements in both $C$ and in $D$ , so $C \cap D = \var{(set4 and set5)}$ .

$C - D$ is the set of all elements in $C$ and not in $D$ , so $C-D = \var {(set4 - set5)}$ .

$(C \cap D) \times (C - D)$ is the set of all pairs of elements $(x,y)$ , where $x$ is in $C \cap D$ and $y$ is in $C - D$ , so $(C \cap D) \times (C-D) = \var{set(product(list(set4 and set5),list(set4 - set5)))}$ .

Similarly, $(D - C) \times (C \cap D) = \var{set(product(list(set5-set4),list(set4 and set5)))}$ .

Finally, $[(C \cap D) \times (C - D)] \cup [(D - C) \times (C \cap D)]$ is the set of all pairs present in either of the above sets, i.e. $\var{set16}$ .

Give a worked solution to the whole question.

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This question is used in the following exam:

Cartesian products and power sets by Lois Rollings in Algebra 1 - Possibilities.

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Lois's copy of set5 - Cartesian Products

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Lois Rollings 7 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

Loading...

Error

Lois's copy of set5 - Cartesian Products

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Lois Rollings 7 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

Generated value: `integer`