Alexander's copy of Andrew's copy of Propositions (v2)

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Alexander Corner

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4 years, 6 months ago

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Alexander Corner 4 years, 6 months ago

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Alexander Corner 4 years, 6 months ago

Created this as a copy of Andrew's copy of Propositions (v2).

Name	Status	Author	Last Modified
Andrew's copy of Propositions (v2)	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Marie's copy of Andrew's copy of Propositions (v2)	draft	Marie Nicholson	17/01/2018 14:08
Propositions (v2)	Ready to use	Marie Nicholson	04/02/2021 15:53
Luis's copy of Andrew's copy of Propositions (v2)	draft	Luis Hernandez	30/11/2018 19:17
Marie's copy of Andrew's copy of Propositions (v2)	draft	Marie Nicholson	04/03/2021 16:43
Propositions with negative marking	Ready to use	Marie Nicholson	04/02/2021 15:25
Valid or invalid argument	Should not be used	Marie Nicholson	04/02/2021 15:26
Alexander's copy of Andrew's copy of Propositions (v2)	Ready to use	Alexander Corner	19/09/2020 20:24

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Question statement

Which of the following are propositions?

Give any introductory information the student needs.

			Name	Type	Generated Value

all	list	Nested 24×3 list
select	list	[ 23, 5, 17, 19, 15, 18 ]
marking_matrix	list	Nested 6×2 list

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Name

Data type

Value

xxxxxxxxxx
 
[
['Every real number is an even integer.','This is a proposition. It is false as there are real numbers which are not even integers, e.g. $1$.',1],
  ['Every even integer is a real number.','A proposition and true.',1],
  ['If $x$ and $y$ are real numbers and $5x=5y$, then $x=y$.','A true proposition as we can cancel off the 5s.',1],
  ['Lions and tigers.','This is not a proposition as there is no truth value we can determine.',0],
  ['Lions and tigers are animals.','This is a true proposition, at least in the standard interpretation of the words.',1],
  ['Some sets are finite.','A true proposition as, for example, the set $\\\{1 \\\}$ is finite.',1],
  ['The smallest positive whole number is 2.','This is a proposition and false, as the smallest positive whole number is $1$.',1],
  ['$x^2=5$.','This is not a proposition: its  truth depends on the value of $x$.',0],
  ['If $n$ is a real number and $n$ is not zero then $n/n=1$.','This a proposition: it is true.',1],
  ['The integer $x$ is a multiple of $7$.','Not a proposition. Its truth depends on the value of $x$.',0],
  ['If the integer $x$ is a multiple of $7$, then it is divisible by $7$.','A true proposition.',1],
  ['Either the integer $x$ is a multiple of $7$, or it is not.','A proposition and true.',1],
  ['Call me Ishmael.','Not a proposition as we cannot ascertain a truth value.',0],
  ['Either $x>3$ or $x<0$.','Not a proposition: its truth depends on the value of $x$.',0],
  ['They like fishcakes.','Not a proposition. Its truth depends on who "They" are.',0],
  ['In the beginning.','Not a proposition: is neither true nor false.',0],
  ['Sheffield Hallam University is a much better place to get your degree.','Not a proposition. It depends on what "better" refers to.',0],
  ['To be or not to be.','Not a proposition: is neither true nor false.',0],
  ['Derby County football club is at its peak.','Not a proposition. It depends on when it is said, and what "peak" means.',0],
  ['Newcastle United finished above Sunderland in the 2014-2015 Season.','A proposition. It is true, according to the records.',1],
  ['England and the UK are two different names for the same place.', 'A proposition. People from England may say it is true. They are wrong.',1],
  ['If $3x^2-2=0$ then $x=\\sqrt{2/3}$ or $x=-\\sqrt{2/3}$','A proposition. It does not depend what $x$ is. It is true.',1],
  ['Numbers $x$, $y$ and $z$ have the property that $x+y=z$.','Not a proposition, as its truth depends on the values of $x$, $y$ and $z$.',0],
  ['Numbers $x$, $y$ and $z$ have the property that $x+y>z$ or $x+y \\le z$.', 'A proposition. One or other of the conditions holds.',1]   
  ]

JME function reference

Description

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

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Generated value: `list`

[ [ "Every real number is an even integer.", "This is a proposition. It is false as there are real numbers which are not even integers, e.g.

$1$ .", 1 ], [ "Every even integer is a real number.", "A proposition and true.", 1 ], [ "If

$x$ and

$y$ are real numbers and

$5x=5y$ , then

$x=y$ .", "A true proposition as we can cancel off the 5s.", 1 ], [ "Lions and tigers.", "This is not a proposition as there is no truth value we can determine.", 0 ], [ "Lions and tigers are animals.", "This is a true proposition, at least in the standard interpretation of the words.", 1 ], [ "Some sets are finite.", "A true proposition as, for example, the set

$\\\{1 \\\}$ is finite.", 1 ], [ "The smallest positive whole number is 2.", "This is a proposition and false, as the smallest positive whole number is

$1$ .", 1 ], [ "

$x^2=5$ .", "This is not a proposition: its truth depends on the value of

$x$ .", 0 ], [ "If

$n$ is a real number and

$n$ is not zero then

$n/n=1$ .", "This a proposition: it is true.", 1 ], [ "The integer

$x$ is a multiple of

$7$ .", "Not a proposition. Its truth depends on the value of

$x$ .", 0 ], [ "If the integer

$x$ is a multiple of

$7$ , then it is divisible by

$7$ .", "A true proposition.", 1 ], [ "Either the integer

$x$ is a multiple of

$7$ , or it is not.", "A proposition and true.", 1 ], [ "Call me Ishmael.", "Not a proposition as we cannot ascertain a truth value.", 0 ], [ "Either

$x>3$ or

$x<0$ .", "Not a proposition: its truth depends on the value of

$x$ .", 0 ], [ "They like fishcakes.", "Not a proposition. Its truth depends on who \"They\" are.", 0 ], [ "In the beginning.", "Not a proposition: is neither true nor false.", 0 ], [ "Sheffield Hallam University is a much better place to get your degree.", "Not a proposition. It depends on what \"better\" refers to.", 0 ], [ "To be or not to be.", "Not a proposition: is neither true nor false.", 0 ], [ "Derby County football club is at its peak.", "Not a proposition. It depends on when it is said, and what \"peak\" means.", 0 ], [ "Newcastle United finished above Sunderland in the 2014-2015 Season.", "A proposition. It is true, according to the records.", 1 ], [ "England and the UK are two different names for the same place.", "A proposition. People from England may say it is true. They are wrong.", 1 ], [ "If

$3x^2-2=0$ then

$x=\\sqrt{2/3}$ or

$x=-\\sqrt{2/3}$ ", "A proposition. It does not depend what

$x$ is. It is true.", 1 ], [ "Numbers

$x$ ,

$y$ and

$z$ have the property that

$x+y=z$ .", "Not a proposition, as its truth depends on the values of

$x$ ,

$y$ and

$z$ .", 0 ], [ "Numbers

$x$ ,

$y$ and

$z$ have the property that

$x+y>z$ or

$x+y \\le z$ .", "A proposition. One or other of the conditions holds.", 1 ] ]

→ Used by:

marking_matrix
select

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"Unnamed part" - Choice text
"Unnamed part" - Choice text
"Unnamed part" - Choice text
"Unnamed part" - Choice text
"Unnamed part" - Choice text
"Unnamed part" - Choice text

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{all[select[0]][0]}
{all[select[1]][0]}
{all[select[2]][0]}
{all[select[3]][0]}
{all[select[4]][0]}
{all[select[5]][0]}

Proposition
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	Proposition	Not a proposition
{all[select[0]][0]}
{all[select[1]][0]}
{all[select[2]][0]}
{all[select[3]][0]}
{all[select[4]][0]}
{all[select[5]][0]}

Advice

For the above we have:

1. {all[select[0]][0]}

{all[select[0]][1]}

2. {all[select[1]][0]}

{all[select[1]][1]}

3. {all[select[2]][0]}

{all[select[2]][1]}

4. {all[select[3]][0]}

{all[select[3]][1]}

5. {all[select[4]][0]}

{all[select[4]][1]}

6. {all[select[5]][0]}

{all[select[5]][1]}

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Alexander's copy of Andrew's copy of Propositions (v2)

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Alexander Corner 4 years, 6 months ago

Alexander Corner 4 years, 6 months ago

Alexander Corner 4 years, 6 months ago

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Alexander's copy of Andrew's copy of Propositions (v2)

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Taxonomy: mathcentre

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Taxonomy: Context

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Alexander Corner 4 years, 6 months ago

Alexander Corner 4 years, 6 months ago

Alexander Corner 4 years, 6 months ago

Error in variable testing condition

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Generated value: list

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Match choices with answers

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Generated value: `list`