Truth tables 3 (v2)-

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Bill Foster 6 years, 4 months ago

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Name	Status	Author	Last Modified
Truth tables 3 (v2)-	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Truth tables 3	draft	Marie Nicholson	04/02/2021 15:25
Louise's copy of Marie's copy of Truth tables 3 (v2)-	draft	Louise Lynch	26/01/2022 19:48
Luis's copy of Truth tables 3 (v2)-	draft	Luis Hernandez	30/11/2018 00:55
Luis's copy of Truth tables 3 (v2)-	draft	Luis Hernandez	30/11/2018 01:00
Crear una tabla de verdad para una expresión lógica de la forma....	Ready to use	Luis Hernandez	06/06/2023 01:11

There are 13 other versions that do you not have access to.

Question statement

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

$((\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1}))\var{op4}(\var{a2} \var{op3} \var{b2}).$

Enter T if true, else enter F.

Give any introductory information the student needs.

			Name	Type	Generated Value

logic_symbol_list	list	[ "p", "q", "not p", "not q" ]
latex_symbol_list	list	List of 4 items
s	list	[ 2, 1, 3, 0, 1, 0 ]

			Name	Type	Generated Value

a	string	\neg p
b	string	q
op	string	\lor
pre_ev1	list	[ true, false, true, true ]
ev1	list	[ "T", "F", "T", "T" ]

			Name	Type	Generated Value

a1	string	\neg q
b1	string	p
op2	string	\lor
pre_ev2	list	[ true, true, false, true ]
ev2	list	[ "T", "T", "F", "T" ]

			Name	Type	Generated Value

p	list	[ true, true, false, false ]
q	list	[ true, false, true, false ]
disp	list	[ "T", "T", "F", "F" ]
disq	list	[ "T", "F", "T", "F" ]

			Name	Type	Generated Value

a2	string	q
b2	string	p
op3	string	\land
pre_ev3	list	[ true, false, false, false ]
ev3	list	[ "T", "F", "F", "F" ]

			Name	Type	Generated Value

op1	string	\to
pre_t_value	list	[ true, true, false, true ]
t_value	list	[ "T", "T", "F", "T" ]

			Name	Type	Generated Value

			final_value	list	[ "T", "F", "F", "F" ]
			op4	string	\land

Automatically regenerate variables?

Name

Data type

Value

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

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" ]

This variable doesn't seem to be used anywhere.

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

Complete the following truth table:

$p$	$q$	$\var{a} \var{op} \var{b}$	$\var{a1} \var{op2} \var{b1}$	$(\var{a} \var{op} \var{b}) \var{op1} (\var{a1} \var{op2} \var{b1})$	$\var{a2} \var{op3} \var{b2}$	$((\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1}))\var{op4}(\var{a2} \var{op3} \var{b2})$
$\var{disp[0]}$	$\var{disq[0]}$	Gap 0.	Gap 4.	Gap 8.	Gap 12.	Gap 16.
$\var{disp[1]}$	$\var{disq[1]}$	Gap 1.	Gap 5.	Gap 9.	Gap 13.	Gap 17.
$\var{disp[2]}$	$\var{disq[2]}$	Gap 2.	Gap 6.	Gap 10.	Gap 14.	Gap 18.
$\var{disp[3]}$	$\var{disq[3]}$	Gap 3.	Gap 7.	Gap 11.	Gap 15.	Gap 19.

Advice

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

$p$	$q$	$\var{a} \var{op} \var{b}$
$\var{disp[0]}$	$\var{disq[0]}$	$\var{ev1[0]}$
$\var{disp[1]}$	$\var{disq[1]}$	$\var{ev1[1]}$
$\var{disp[2]}$	$\var{disq[2]}$	$\var{ev1[2]}$
$\var{disp[3]}$	$\var{disq[3]}$	$\var{ev1[3]}$

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

$p$	$q$	$\var{a1} \var{op2} \var{b1}$
$\var{disp[0]}$	$\var{disq[0]}$	$\var{ev2[0]}$
$\var{disp[1]}$	$\var{disq[1]}$	$\var{ev2[1]}$
$\var{disp[2]}$	$\var{disq[2]}$	$\var{ev2[2]}$
$\var{disp[3]}$	$\var{disq[3]}$	$\var{ev2[3]}$

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

$p$	$q$	$\var{a} \var{op} \var{b}$	$\var{a1} \var{op2} \var{b1}$	$(\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1})$
$\var{disp[0]}$	$\var{disq[0]}$	$\var{ev1[0]}$	$\var{ev2[0]}$	$\var{t_value[0]}$
$\var{disp[1]}$	$\var{disq[1]}$	$\var{ev1[1]}$	$\var{ev2[1]}$	$\var{t_value[1]}$
$\var{disp[2]}$	$\var{disq[2]}$	$\var{ev1[2]}$	$\var{ev2[2]}$	$\var{t_value[2]}$
$\var{disp[3]}$	$\var{disq[3]}$	$\var{ev1[3]}$	$\var{ev2[3]}$	$\var{t_value[3]}$

Next we find the truth table for $\var{a2} \var{op3} \var{b2}$ :

$p$	$q$	$\var{a2} \var{op3} \var{b2}$
$\var{disp[0]}$	$\var{disq[0]}$	$\var{ev3[0]}$
$\var{disp[1]}$	$\var{disq[1]}$	$\var{ev3[1]}$
$\var{disp[2]}$	$\var{disq[2]}$	$\var{ev3[2]}$
$\var{disp[3]}$	$\var{disq[3]}$	$\var{ev3[3]}$

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

$p$	$q$	$(\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1})$	$\var{a2} \var{op3} \var{b2}$	$((\var{a} \var{op} \var{b})\var{op1}(\var{a1} \var{op2} \var{b1}))\var{op4}(\var{a2} \var{op3} \var{b2})$
$\var{disp[0]}$	$\var{disq[0]}$	$\var{t_value[0]}$	$\var{ev3[0]}$	$\var{final_value[0]}$
$\var{disp[1]}$	$\var{disq[1]}$	$\var{t_value[1]}$	$\var{ev3[1]}$	$\var{final_value[1]}$
$\var{disp[2]}$	$\var{disq[2]}$	$\var{t_value[2]}$	$\var{ev3[2]}$	$\var{final_value[2]}$
$\var{disp[3]}$	$\var{disq[3]}$	$\var{t_value[3]}$	$\var{ev3[3]}$	$\var{final_value[3]}$

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Bill Foster 6 years, 4 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 3 (v2)-

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 4 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`