Assignment: Constructing Truth Tables
In this assignment, you will construct truth tables and use them to assess the validity of arguments.
1. Premise: P → Q
Conclusion: ~P → ~Q
| P |
Q |
P → Q |
~P → ~Q |
| T |
T |
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| T |
F |
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| F |
T |
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| F |
F |
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2. Premise: P → Q
Conclusion: ~Q → ~P
| P |
Q |
P → Q |
~Q → ~P |
| T |
T |
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| T |
F |
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| F |
T |
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| F |
F |
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3. Premise: (P & Q) → R
Q → R
Conclusion: P → R
| P |
Q |
R |
P & Q |
(P & Q) → R |
Q → R |
P → R |
| T |
T |
T |
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| T |
T |
F |
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| T |
F |
T |
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| T |
F |
F |
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| F |
T |
T |
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| F |
T |
F |
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| F |
F |
T |
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| F |
F |
F |
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4. Translate the following argument and use truth tables to test for validity.
"If 9 is less than 10 and every odd number less than 10 is divisible by 3, then 9 is divisible by 3. THEREFORE If 9 is less than 10 it is less than 10 it is divisible by 3."
N = "9 is less than 10"
O = "Every odd number less than 10 is divisible by 3."
D = "9 is divisible by 3."
Premise:
Conclusion:
5. Translate the following argument and use truth tables to test for validity.
"If it rains tomorrow, I will have a tough commute. If it snows tomorrow, I will have a tough commute. It will either rain or snow tomorrow. THEREFORE I will have a tough commute."
R = "It rains tomorrow."
S = "It snows tomorrow."
T = "I will have a tough commute."
Premise:
Conclusion: