This document provides 5 practice truth table exercises to test the validity of arguments: 1) Tests the argument ~P → ~Q with premises P → Q 2) Tests the argument ~Q → ~P with premises P → Q 3) Tests the argument P → R with premises (P & Q) → R and Q → R 4) Translates and tests the argument that if N and O then D, with N = '9 is less than 10', O = 'Every odd number less than 10 is divisible by 3', and D = '9 is divisible by 3' 5) Translates and tests the argument that if R or S then T, with R = 'It rains tomorrow',

1. M5.A1 Truth Table Exercises
Back-up QUESTION SET

2. 1

3. Premise:
P
→ Q
Conclusion:
~P
→ ~Q

4. Answer:

5. P
Q

8. 2
Premise:
P
→ Q
Conclusion:
~Q
→ ~P

9. Answer:

10. P
Q

12. 3
Premise:
(P & Q)
→ R

13. Q
→
R
Conclusion:
P
→
R

14. P
Q
R

18. 4
Translate the following argument and use truth tables to test for
validity.

19. "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"

20. O = "Every odd number less than 10 is divisible by 3."
D =
"9 is divisible by 3."

21. Premise:
Conclusion:

22. N
O
D

25. 5. Translate the following argument and use truth tables to test
for validity.

26. "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."

27. S =
"It snows tomorrow."
T =
"I will have a tough commute."
Premise:

29. Conclusion
ANSWER:
R
S
T