Set 2-3

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Mark Hodds

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Mark Hodds 8 years, 6 months ago

Created this as a copy of set3.

Name	Status	Author	Last Modified
set3	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Set 2-3	draft	Mark Hodds	30/10/2016 20:05
Luis's copy of set3	draft	Luis Hernandez	30/11/2018 17:36
Lois's copy of Set 2-3	draft	Lois Rollings	05/06/2019 16:07

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Question statement

In this question, the universal set is $\mathcal{U}=\{x \in \mathbb{N}\; | \;x \leq \var{a}\}$ .

Let:

$A=\{x \in \mathbb{N}\;|\;\var{b}\leq x \leq \var{c}\}$ .

$B=\{x \in \mathbb{N}\;|\;x \gt \var{d}\}$ .

$C=\{ x \in \mathbb{N}\;|\; x \text{ divisible by } \var{f}\}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	20
b	integer	7
c	integer	19
d	integer	17
f	integer	5
universal	set	Set of 20 items
set1	set	Set of 13 items
set2	set	set(18,19,20)
set3	set	set(5,10,15,20)

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(15..30)

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:

c
set2
set3
universal

This variable doesn't seem to be used anywhere.

Parts

Gap-fill

Gap-fill

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

Enumerate the following sets:

a) $A \cap B=\;$ Gap 0.

b) $B \cap C=\;$ Gap 1.

c) $A \cap C^{c}=\;$ Gap 2.

d) $(A^{c} \cup C) \cap B=\;$ Gap 3.

e) $(A \cup C)^{c} \cap B^{c}=\;$ Gap 4.

f) $(A \cup B^{c}) \cap C=\;$ Gap 5.

Note that you input sets in the form set(a,b,c,..,z) .

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

The empty set is input as set().

Also some labour saving tips:

If you want to input all integers between $a$ and $b$ inclusive then instead of writing all the elements you can input this as set(a..b).

If you want to input all integers between $a$ and $b$ inclusive in steps of $c$ then this is input as set(a..b#c). So all odd integers from $-3$ to $28$ are input as set(-3..28#2).

Advice

Give a worked solution to the whole question.

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This question is used in the following exams:

Sets by Mark Hodds in 101MP 2018.
101MP 2019 - Sets Week 5 by Mark Hodds in 101MP 2018.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Mark Hodds 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Set 2-3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Mark Hodds 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`