M5.A1 Truth Table Exercises 
Backup QUESTION SET 
1 
Premise: 
P → Q 
Conclusion: 
~P → ~Q 
P 
Q 
P → Q 
~P → ~Q 
T 
T 
T 
F 
F 
T 
F 
F 
2 
Premise: 
P → Q 
Conclusion: 
~Q → ~P 
P 
Q 
P → Q 
~Q → ~P 
T 
T 
T 
F 
F 
T 
F 
F 
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 
T 
T 
F 
T 
F 
T 
T 
F 
F 
F 
T 
T 
F 
T 
F 
F 
F 
T 
F 
F 
F 
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: 
N 
O 
D 



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 
ANSWER: 
R 
S 
T 


