“Use truth tables to determine the validity or invalidity of each of the following argument forms”
Note: Lines which contain true premises and a true conclusion are in green, while lines with true premises and a false conclusion are in red.
1. Valid.
P  Q  P ∧ Q  

T 
T 
T 
V 
T 
F 
F 

F 
F 
F 

F 
T 
F 
2. Invalid.
P  Q  P ∧ Q  

T 
T 
T 
V 
T 
F 
F 
X 
F 
F 
F 

F 
T 
F 
3. Invalid.
P  Q  P ∨ Q  

T 
T 
T 
V 
T 
F 
T 
V 
F 
T 
T 
X 
F 
T 
F 
4. Valid.
P  P ∨ Q  Q  

T 
T 
T 
V 
F 
T 
T 

T 
T 
F 
V 
F 
F 
F 
5. Invalid.
P  Q  P→Q  

T 
T 
T 
V 
T 
F 
F 
X 
F 
T 
T 

F 
F 
T 
6. Valid.
P  Q  Q→P  

T 
T 
T 
V 
T 
F 
T 
V 
F 
T 
F 

F 
F 
T 
7. Valid.
P  Q 
¬Q 
¬P 
P→Q 
¬Q→¬P 


T 
T 
F 
F 
T 
T 
V 
T 
F 
T 
F 
F 
F 

F 
T 
F 
T 
T 
T 
V 
F 
F 
T 
T 
T 
T 
V 
8. Invalid.
P  Q 
¬Q 
¬P 
P→Q 
¬P→¬Q 


T 
T 
F 
F 
T 
T 
V 
T 
F 
T 
F 
F 
T 

F 
T 
F 
T 
T 
F 
X 
F 
F 
T 
T 
T 
T 
V 
9. Valid.
P  Q  R  P→(Q ∧ R)  ¬(Q ∧ R)→ ¬P  Q ∧ R  ¬(Q ∧ R)  ¬P  

T 
T 
T 
T 
T 
T 
F 
F 
V 
T 
T 
F 
F 
F 
F 
T 
F 

T 
F 
F 
F 
F 
F 
T 
F 

T 
F 
T 
T 
T 
F 
T 
T 
V 
F 
F 
F 
T 
T 
F 
T 
T 
V 
F 
F 
T 
T 
T 
T 
F 
T 
V 
T 
F 
T 
F 
F 
F 
T 
F 

F 
T 
F 
T 
T 
F 
T 
T 
10. Invalid.
P  Q  ¬Q  P ∨ Q  

T 
T 
F 
T 
X 
T 
F 
T 
T 
V 
F 
T 
F 
T 

F 
F 
T 
F 
11. Valid.
P  Q  P ∧ Q  

T 
T 
T 
V 
T 
F 
F 

F 
T 
F 

F 
F 
F 
12. Invalid.
P  Q  P→Q  Q→P  P v Q  

T 
T 
T 
T 
T 
V 
T 
F 
F 
T 
T 

F 
T 
T 
F 
T 

F 
F 
T 
T 
F 
X 
13. Valid.
P  Q  P→Q  Q v P  

T 
T 
T 
T 
V 
T 
F 
F 
T 

F 
T 
T 
T 
V 
F 
F 
T 
F 
14. Valid.
P  Q  R  P→Q  Q→R  P→(Q→R)  P→R  

T 
T 
T 
T 
T 
T 
T 
V 
T 
T 
F 
T 
F 
F 
F 

T 
F 
F 
F 
T 
T 
F 

F 
F 
F 
T 
T 
T 
T 
V 
F 
F 
T 
T 
T 
T 
T 
V 
F 
T 
T 
T 
T 
T 
T 
V 
F 
T 
F 
T 
F 
T 
T 
V 
T 
F 
T 
F 
T 
T 
T 
15. Valid.
P  Q  R  P→Q  P→R  Q v R  (P→Q) ∧ (P→R)  

T 
T 
T 
T 
T 
T 
T 
V 
T 
T 
F 
T 
F 
T 
F 

T 
F 
F 
F 
F 
F 
F 

F 
F 
F 
T 
T 
F 
T 

F 
F 
T 
T 
T 
T 
T 

F 
T 
T 
T 
T 
T 
T 

F 
T 
F 
T 
T 
T 
T 

T 
F 
T 
F 
T 
T 
F 
16. Invalid.
P  Q  R  Q v R  P→(Q vR)  P→¬Q  P v R  ¬Q  

T 
T 
T 
T 
T 
F 
T 
F 

T 
T 
F 
T 
T 
T 
T 
F 
V 
T 
F 
F 
F 
T 
T 
T 
T 
V 
F 
F 
F 
F 
T 
T 
F 
T 
X 
F 
F 
T 
T 
T 
T 
T 
T 
V 
F 
T 
T 
T 
T 
T 
T 
F 
V 
F 
T 
F 
T 
T 
T 
F 
F 
X 
T 
F 
T 
T 
T 
T 
T 
T 
V 
17. Valid.
P  Q  R  S  P→Q  R→S  (P→Q) ∧ (R→S)  P v R  Q v S  

T 
T 
T 
T 
T 
T 
T 
T 
T 
V 
T 
T 
T 
F 
T 
F 
F 
T 
T 

T 
T 
F 
F 
T 
T 
T 
T 
T 
V 
T 
F 
F 
F 
T 
T 
T 
T 
T 

T 
T 
F 
T 
T 
T 
T 
T 
T 
V 
T 
F 
T 
T 
F 
T 
F 
T 
T 

T 
F 
F 
T 
F 
T 
F 
T 
T 

T 
F 
T 
F 
F 
F 
F 
T 
F 

F 
F 
F 
F 
T 
T 
T 
F 
F 

F 
F 
F 
T 
T 
T 
T 
F 
T 

F 
F 
T 
T 
T 
T 
T 
T 
T 
V 
F 
T 
T 
T 
T 
T 
T 
T 
T 
V 
F 
F 
T 
F 
T 
F 
F 
T 
F 

F 
T 
F 
F 
T 
T 
T 
F 
T 

F 
T 
T 
F 
T 
F 
F 
T 
T 

F 
T 
F 
T 
T 
T 
T 
F 
T 
18. Valid.
P  Q  R  S  P→Q  R→S  (P→Q) ∧ (R→S)  ¬P v ¬R  ¬Q v ¬S 
¬P 
¬Q 
¬R 
¬S 


T 
T 
T 
T 
T 
T 
T 
F 
F 
F 
F 
F 
F 

T 
T 
T 
F 
T 
F 
F 
F 
T 
F 
F 
F 
T 

T 
T 
F 
F 
T 
T 
T 
T 
T 
F 
F 
T 
T 
V 
T 
F 
F 
F 
T 
T 
T 
T 
F 
F 
T 
T 
T 

T 
T 
F 
T 
T 
T 
T 
T 
F 
F 
F 
T 
F 

T 
F 
T 
T 
F 
T 
F 
F 
T 
F 
T 
F 
F 

T 
F 
F 
T 
F 
T 
F 
T 
T 
F 
T 
T 
F 

T 
F 
T 
F 
F 
F 
F 
F 
T 
F 
T 
F 
T 

F 
F 
F 
F 
T 
T 
T 
T 
T 
T 
T 
T 
T 
V 
F 
F 
F 
T 
T 
T 
T 
T 
T 
T 
T 
T 
F 
V 
F 
F 
T 
T 
T 
T 
T 
T 
T 
T 
T 
F 
F 
V 
F 
T 
T 
T 
T 
T 
T 
T 
F 
T 
F 
F 
F 

F 
F 
T 
F 
T 
F 
F 
T 
T 
T 
T 
F 
T 

F 
T 
F 
F 
T 
T 
T 
T 
T 
T 
F 
T 
T 
V 
F 
T 
T 
F 
T 
F 
F 
T 
T 
T 
F 
F 
T 

F 
T 
F 
T 
T 
T 
T 
T 
F 
T 
F 
T 
F 
19. Valid.
P  Q  P v Q  P ∧ Q  (P v Q)→(P ∧ Q)  

T 
T 
T 
T 
T 
V 
T 
F 
T 
F 
F 

F 
T 
T 
F 
F 

F 
F 
F 
F 
T 
20. Valid.
P  Q  ¬P  (Q ∧ ¬P)  P v (Q ∧ ¬P)  ¬(Q ∧ ¬P)  

T 
T 
F 
F 
T 
T 
V 
T 
F 
F 
F 
T 
T 
V 
F 
T 
T 
T 
T 
F 

F 
F 
T 
F 
F 
T 
21. Valid.
P  Q  P v Q  P ∧ Q  (P v Q)→(P ∧ Q)  ¬(P v Q)  ¬(P ∧ Q)  

T 
T 
T 
T 
T 
F 
F 

T 
F 
T 
F 
F 
F 
T 

F 
T 
T 
F 
F 
F 
T 

F 
F 
F 
F 
T 
T 
T 
V 