Truth tables 4 (v2)

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Bill Foster

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6 years, 5 months ago

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Christian Lawson-Perfect 5 years, 10 months ago

Saved a checkpoint:

Can't convert grids of booleans to matrices automatically any more, so I've added a function 'bool_matrix' to do that.

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Bill Foster 6 years, 5 months ago

Gave some feedback: Ready to use

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

Name	Status	Author	Last Modified
Truth tables 4 (v2)	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Truth tables 4	draft	Marie Nicholson	04/02/2021 15:25
Luis's copy of Truth tables 4 (v2)	draft	Luis Hernandez	30/11/2018 00:54
Construir la tabla de verdad de una proposición compuesta	Ready to use	Luis Hernandez	02/12/2020 15:42

There are 11 other versions that do you not have access to.

Question statement

In the following question you are asked to construct a truth table for:

$((\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1}))\var{op4}\var{a2}.$

Enter T if true, else enter F.

Give any introductory information the student needs.

			Name	Type	Generated Value

logic_symbol_list	list	List of 6 items
latex_symbol_list	list	List of 6 items
s	list	[ 4, 0, 0, 2, 2, 1 ]

			Name	Type	Generated Value

a	string	r
b	string	p
op	string	\lor
pre_ev1	list	List of 8 items
ev1	list	List of 8 items

			Name	Type	Generated Value

a1	string	p
b1	string	\neg p
op2	string	\land
pre_ev2	list	List of 8 items
ev2	list	List of 8 items

			Name	Type	Generated Value

p	list	List of 8 items
q	list	List of 8 items
r	list	List of 8 items
bool_p	list	List of 8 items
bool_q	list	List of 8 items
bool_r	list	List of 8 items

			Name	Type	Generated Value

a2	string	\neg p
pre_ev3	list	List of 8 items
c2	string	p
d2	list	List of 8 items
ev3	list	List of 8 items

			Name	Type	Generated Value

op1	string	\land
pre_t_value	list	List of 8 items
t_value	list	List of 8 items

			Name	Type	Generated Value

pre_final_value	list	List of 8 items
op4	string	\lor
logic_values	matrix	Matrix of size 3×8
final_value	list	List of 8 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
["p","q","not p","not q","r","not r"]

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: `list`

[ "p", "q", "not p", "not q", "r", "not r" ]

This variable doesn't seem to be used anywhere.

Parts

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1. Gap Gap 0. Match text pattern
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2. Gap Gap 1. Match text pattern
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3. Gap Gap 2. Match text pattern
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4. Gap Gap 3. Match text pattern
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6. Gap Gap 5. Match text pattern
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7. Gap Gap 6. Match text pattern
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8. Gap Gap 7. Match text pattern
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Gap-fill

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

Complete the following truth table:

$p$	$q$	$r$	$((\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1}))\var{op4}\var{a2}$
$\var{p[0]}$	$\var{q[0]}$	$\var{r[0]}$	Gap 0.
$\var{p[1]}$	$\var{q[1]}$	$\var{r[1]}$	Gap 1.
$\var{p[2]}$	$\var{q[2]}$	$\var{r[2]}$	Gap 2.
$\var{p[3]}$	$\var{q[3]}$	$\var{r[3]}$	Gap 3.
$\var{p[4]}$	$\var{q[4]}$	$\var{r[4]}$	Gap 4.
$\var{p[5]}$	$\var{q[5]}$	$\var{r[5]}$	Gap 5.
$\var{p[6]}$	$\var{q[6]}$	$\var{r[6]}$	Gap 6.
$\var{p[7]}$	$\var{q[7]}$	$\var{r[7]}$	Gap 7.

Advice

First we find the truth table for $\var{a} \var{op} \var{b}$ :

$p$	$q$	$r$	$\var{a} \var{op} \var{b}$
$\var{p[0]}$	$\var{q[0]}$	$\var{r[0]}$	$\var{ev1[0]}$
$\var{p[1]}$	$\var{q[1]}$	$\var{r[1]}$	$\var{ev1[1]}$
$\var{p[2]}$	$\var{q[2]}$	$\var{r[2]}$	$\var{ev1[2]}$
$\var{p[3]}$	$\var{q[3]}$	$\var{r[3]}$	$\var{ev1[3]}$
$\var{p[4]}$	$\var{q[4]}$	$\var{r[4]}$	$\var{ev1[4]}$
$\var{p[5]}$	$\var{q[5]}$	$\var{r[5]}$	$\var{ev1[5]}$
$\var{p[6]}$	$\var{q[6]}$	$\var{r[6]}$	$\var{ev1[6]}$
$\var{p[7]}$	$\var{q[7]}$	$\var{r[7]}$	$\var{ev1[7]}$

Then the truth table for $\var{a1} \var{op2} \var{b1}$ :

$p$	$q$	$r$	$\var{a1} \var{op2} \var{b1}$
$\var{p[0]}$	$\var{q[0]}$	$\var{r[0]}$	$\var{ev2[0]}$
$\var{p[1]}$	$\var{q[1]}$	$\var{r[1]}$	$\var{ev2[1]}$
$\var{p[2]}$	$\var{q[2]}$	$\var{r[2]}$	$\var{ev2[2]}$
$\var{p[3]}$	$\var{q[3]}$	$\var{r[3]}$	$\var{ev2[3]}$
$\var{p[4]}$	$\var{q[4]}$	$\var{r[4]}$	$\var{ev2[4]}$
$\var{p[5]}$	$\var{q[5]}$	$\var{r[5]}$	$\var{ev2[5]}$
$\var{p[6]}$	$\var{q[6]}$	$\var{r[6]}$	$\var{ev2[6]}$
$\var{p[7]}$	$\var{q[7]}$	$\var{r[7]}$	$\var{ev2[7]}$

Putting these together to find $(\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1})$ :

$p$	$q$	$r$	$\var{a} \var{op} \var{b}$	$\var{a1} \var{op2} \var{b1}$	$(\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1})$
$\var{p[0]}$	$\var{q[0]}$	$\var{r[0]}$	$\var{ev1[0]}$	$\var{ev2[0]}$	$\var{t_value[0]}$
$\var{p[1]}$	$\var{q[1]}$	$\var{r[1]}$	$\var{ev1[1]}$	$\var{ev2[1]}$	$\var{t_value[1]}$
$\var{p[2]}$	$\var{q[2]}$	$\var{r[2]}$	$\var{ev1[2]}$	$\var{ev2[2]}$	$\var{t_value[2]}$
$\var{p[3]}$	$\var{q[3]}$	$\var{r[3]}$	$\var{ev1[3]}$	$\var{ev2[3]}$	$\var{t_value[3]}$
$\var{p[4]}$	$\var{q[4]}$	$\var{r[4]}$	$\var{ev1[4]}$	$\var{ev2[4]}$	$\var{t_value[4]}$
$\var{p[5]}$	$\var{q[5]}$	$\var{r[5]}$	$\var{ev1[5]}$	$\var{ev2[5]}$	$\var{t_value[5]}$
$\var{p[6]}$	$\var{q[6]}$	$\var{r[6]}$	$\var{ev1[6]}$	$\var{ev2[6]}$	$\var{t_value[6]}$
$\var{p[7]}$	$\var{q[7]}$	$\var{r[7]}$	$\var{ev1[7]}$	$\var{ev2[7]}$	$\var{t_value[7]}$

Next we find the truth table for $\var{a2}$ :

$\var{c2}$	$\var{a2}$
$\var{d2[0]}$	$\var{ev3[0]}$
$\var{d2[1]}$	$\var{ev3[1]}$
$\var{d2[2]}$	$\var{ev3[2]}$
$\var{d2[3]}$	$\var{ev3[3]}$
$\var{d2[4]}$	$\var{ev3[4]}$
$\var{d2[5]}$	$\var{ev3[5]}$
$\var{d2[6]}$	$\var{ev3[6]}$
$\var{d2[7]}$	$\var{ev3[7]}$

Putting this all together to obtain the truth table we want:

$p$	$q$	$r$	$(\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1})$	$\var{a2}$	$((\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1}))\var{op4}\var{a2}$
$\var{p[0]}$	$\var{q[0]}$	$\var{r[0]}$	$\var{t_value[0]}$	$\var{ev3[0]}$	$\var{final_value[0]}$
$\var{p[1]}$	$\var{q[1]}$	$\var{r[1]}$	$\var{t_value[1]}$	$\var{ev3[1]}$	$\var{final_value[1]}$
$\var{p[2]}$	$\var{q[2]}$	$\var{r[2]}$	$\var{t_value[2]}$	$\var{ev3[2]}$	$\var{final_value[2]}$
$\var{p[3]}$	$\var{q[3]}$	$\var{r[3]}$	$\var{t_value[3]}$	$\var{ev3[3]}$	$\var{final_value[3]}$
$\var{p[4]}$	$\var{q[4]}$	$\var{r[4]}$	$\var{t_value[4]}$	$\var{ev3[4]}$	$\var{final_value[4]}$
$\var{p[5]}$	$\var{q[5]}$	$\var{r[5]}$	$\var{t_value[5]}$	$\var{ev3[5]}$	$\var{final_value[5]}$
$\var{p[6]}$	$\var{q[6]}$	$\var{r[6]}$	$\var{t_value[6]}$	$\var{ev3[6]}$	$\var{final_value[6]}$
$\var{p[7]}$	$\var{q[7]}$	$\var{r[7]}$	$\var{t_value[7]}$	$\var{ev3[7]}$	$\var{final_value[7]}$

Give a worked solution to the whole question.

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Taxonomy: mathcentre

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Christian Lawson-Perfect 5 years, 10 months ago

Bill Foster 6 years, 5 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `list`

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Gap-fill

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Truth tables 4 (v2)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 5 years, 10 months ago

Bill Foster 6 years, 5 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`