Truth tables 2

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Marie Nicholson

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Marie Nicholson 7 years, 2 months ago

Created this as a copy of Truth tables 2 (v2) -.

Name	Status	Author	Last Modified
Truth tables 2 (v2) -	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Daniel's copy of Truth tables 2 (v2) -	draft	Daniel Mansfield	29/08/2017 02:39
Truth tables 2	draft	Marie Nicholson	04/02/2021 15:25
Luis's copy of Truth tables 2 (v2) -	draft	Luis Hernandez	30/11/2018 00:56
Luis's copy of Truth tables 2 (v2) -	draft	Luis Hernandez	30/11/2018 00:58
Truth tables quiz	Ready to use	Marie Nicholson	10/12/2021 19:02

There are 21 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	[ "p", "q", "not p", "not q" ]
latex_symbol_list	list	List of 4 items
s	list	[ 1, 0, 3, 2, 3, 3 ]

			Name	Type	Generated Value

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

			Name	Type	Generated Value

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

			Name	Type	Generated Value

p	list	[ "T", "T", "F", "F" ]
q	list	[ "T", "F", "T", "F" ]
bool_p	list	[ true, true, false, false ]
bool_q	list	[ true, false, true, false ]

			Name	Type	Generated Value

a2	string	\neg q
pre_ev3	list	[ false, true, false, true ]
ev3	list	[ "F", "T", "F", "T" ]

			Name	Type	Generated Value

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

			Name	Type	Generated Value

pre_final_value	list	[ false, true, true, true ]
op4	string	\to
final_value	list	[ "F", "T", "T", "T" ]

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:

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

Advice

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

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

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

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

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

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

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

$p$	$q$	$\var{a2}$
$\var{p[0]}$	$\var{q[0]}$	$\var{ev3[0]}$
$\var{p[1]}$	$\var{q[1]}$	$\var{ev3[1]}$
$\var{p[2]}$	$\var{q[2]}$	$\var{ev3[2]}$
$\var{p[3]}$	$\var{q[3]}$	$\var{ev3[3]}$

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

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

Give a worked solution to the whole question.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

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Checkpoint description

Marie Nicholson 7 years, 2 months ago

Error in variable testing condition

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Generated value: `list`

Parts

Gap-fill

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Truth tables 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Marie Nicholson 7 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`