Exercises Study 5: truth tables
Exercise 5.1: Truth Table - Functions
Part A Instructions: Match the truth table values in the columns, a through g, with the correct forms, 1 through 7.
Part A Instructions: Match the truth table values in the columns, a through g, with the correct forms, 1 through 7.
x |
y |
a |
b |
c |
d |
e |
f |
g |
T |
T |
T |
T |
F |
F |
T |
F |
F |
T |
F |
F |
F |
T |
T |
T |
F |
F |
F |
T |
T |
F |
T |
F |
T |
F |
T |
F |
F |
T |
F |
T |
F |
F |
T |
T |
1. conjunction. _____
2. disjunction. _____
3. implication. _____
4. contradiction of conjunction. _____
5. contradiction of disjunction. _____
6. contradiction of implication. _____
7. contradiction of x. _____
2. disjunction. _____
3. implication. _____
4. contradiction of conjunction. _____
5. contradiction of disjunction. _____
6. contradiction of implication. _____
7. contradiction of x. _____
Part B Instructions: Match the truth table values in the columns, a through g, with the correct forms, 1 through 10.
p |
q |
a |
b |
c |
d |
e |
f |
g |
T |
T |
T |
F |
F |
T |
T |
T |
F |
T |
F |
T |
F |
T |
F |
F |
T |
F |
F |
T |
T |
F |
T |
T |
F |
F |
F |
F |
F |
T |
F |
T |
T |
F |
F |
T |
1. (p + q) '. _____
2. (pp' ) '. _____
3. (p + p ' ) '. _____
4. (pq) '. _____
5. (p ' + q). _____
6. (pq ' ) '. _____
7. (p ' + q ' ). _____
8. (p ' + q ' ) '. _____
9. (p < p ' ) '. _____
10. (p ' + p ' ) '. _____
2. (pp' ) '. _____
3. (p + p ' ) '. _____
4. (pq) '. _____
5. (p ' + q). _____
6. (pq ' ) '. _____
7. (p ' + q ' ). _____
8. (p ' + q ' ) '. _____
9. (p < p ' ) '. _____
10. (p ' + p ' ) '. _____
Exercise 5.2: Truth Table Analysis
Instructions: Do a truth table analysis of the following propositions.
Hawk Newton is good in either science or theology, but not both. Moreover, either he is good at logic or bad at theology. If he is not good in science, he is bad at theology. If he is bad at theology, he is good at logic.
What do these four premises imply, if anything? Is Hawk good in anything? In or at what?
1. Hawk is good in either science or theology, but not both. (s + t) (st)'
2. Hawk is good at logic or bad at theology. (l + t')
3. If he is not good in science, he is bad at theology. (s' < t')
4. If he is bad at theology, he is good at logic. (t' < l)
Instructions: Do a truth table analysis of the following propositions.
Hawk Newton is good in either science or theology, but not both. Moreover, either he is good at logic or bad at theology. If he is not good in science, he is bad at theology. If he is bad at theology, he is good at logic.
What do these four premises imply, if anything? Is Hawk good in anything? In or at what?
1. Hawk is good in either science or theology, but not both. (s + t) (st)'
2. Hawk is good at logic or bad at theology. (l + t')
3. If he is not good in science, he is bad at theology. (s' < t')
4. If he is bad at theology, he is good at logic. (t' < l)
|
Variables |
1st |
2nd |
3rd |
4th |
||
|
s |
l |
t |
(s + t) (st)' |
(l + t') |
(s' < t') |
(t' < l) |
1 |
T |
T |
T |
|
|
|
|
2 |
T |
T |
F |
|
|
|
|
3 |
T |
F |
T |
|
|
|
|
4 |
T |
F |
F |
|
|
|
|
5 |
F |
T |
T |
|
|
|
|
6 |
F |
T |
F |
|
|
|
|
7 |
F |
F |
T |
|
|
|
|
8 |
F |
F |
F |
|
|
|
|
|
i |
ii |
iii |
iv |
v |
vi |
vii |
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