Introduction to Logic

Truth-Tables III

Please fill in the missing truth-values in each of the following truth tables:

1.
C
D
E
(C v D)
~E
(C v D) ~E
 
T
T
T
F
F
 
T
T
F
T
T
T
 
T
F
T
T
F
F
 
F
F
T
T
T
 
F
T
T
T
F
F
 
F
T
F
T
T
T
 
F
F
T
F
F
F
 
F
F
F
T
F

2.
P
Q
R
Q v R
~(Q v R)
P v (Q v R)
 
T
T
T
T
F
T
 
T
F
T
F
T
T
T
T
F
T
T
F
F
T
T
F
T
T
T
F
F
 
F
T
F
T
F
F
 
F
F
T
T
F
F
 
F
F
F
F
T
F
 

3.
C
D
E
(C v D)
~E
(C v D) ~E
 
T
T
T
F
F
 
T
T
T
T
T
 
T
F
T
F
F
 
T
F
F
T
T
T
 
F
T
T
T
F
F
 
F
T
F
T
T
T
 
F
F
T
F
F
F
 
F
F
F
F
T
F
 

4.

C
D
E
(C v D)
~E
(C v D) ~E
 
T
T
T
F
F
 
T
T
F
T
T
 
T
F
T
F
F
 
T
F
F
T
T
 
F
T
T
T
F
F
 
F
T
F
T
T
T
 
F
F
T
F
F
F
 
F
F
F
F
T
F
 


5.
P
Q
R
Q v R
~(Q v R)
P v (Q v R)
 
T
T
T
T
F
T
 
T
T
F
T
F
T
 
T
F
T
F
T
T
F
F
T
T
F
T
T
F
F
F
T
F
T
F
F
 
F
F
T
T
F
F
 
F
F
F
F
T
F
 

6.
C
D
E
(C v D)
~E
(C v D) ~E
 
T
T
T
T
F
F
 
T
T
F
T
T
T
 
T
F
T
T
F
F
 
T
F
F
T
T
T
 
F
T
T
T
F
F
 
F
T
F
T
T
F
F
T
F
F
F
F
F
T
F

7.

C
D
E
(C v D)
~E
(C v D) ~E
 
T
T
T
T
F
 
T
T
F
T
T
 
T
F
T
T
F
 
T
F
F
T
T
 
F
T
T
T
F
F
 
F
T
F
T
T
T
 
F
F
T
F
F
F
 
F
F
F
F
T
F
 

8.
P
Q
R
Q v R
~(Q v R)
P v (Q v R)
 
T
T
T
T
T
T
T
F
T
T
T
F
T
T
T
T
F
F
F
T
F
T
T
T
F
F
T
F
T
F
F
 
F
F
T
T
F
F
 
F
F
F
F
T
F
 

9.
C
D
E
(C v D)
~E
(C v D) ~E
 
T
T
T
T
F
 
T
T
F
T
T
 
T
F
T
T
F
 
T
F
F
T
T
 
F
T
T
T
F
F
 
F
T
F
T
T
T
 
F
F
T
F
F
F
 
F
F
F
F
T
F
 

10.
C
D
E
(C v D)
~E
(C v D) ~E
 
T
T
T
T
F
 
T
T
F
T
T
 
T
F
T
T
F
 
T
F
F
T
T
 
F
T
T
T
F
F
T
F
T
T
F
F
T
F
F
F
F
F
F
T

11.
P
Q
R
Q v R
~(Q v R)
P v (Q v R)
 
T
T
T
T
F
T
T
F
T
F
T
F
T
T
F
T
F
F
F
T
F
T
T
T
F
F
T
F
T
F
F
F
T
T
F
F
F
F
F
T

12.
C
D
E
(C v D)
~E
(C v D) ~E
 
T
T
T
T
F
F
 
T
T
F
T
T
T
 
T
F
T
T
F
F
 
T
F
F
T
T
T
 
F
T
T
T
F
F
T
F
T
T
F
F
T
F
F
F
F
F
F
T

13.
C
D
E
(C v D)
~E
(C v D) ~E
 
T
T
T
T
F
F
 
T
T
F
T
T
T
 
T
F
T
T
F
F
 
T
F
F
T
T
T
 
F
T
T
F
F
F
T
F
T
T
F
F
T
F
F
F
F
F
T
F

14.
P
Q
R
Q v R
~(Q v R)
P v (Q v R)
 
T
T
T
F
T
T
T
F
F
T
T
F
T
F
T
T
F
F
T
T
F
T
T
F
F
F
T
F
T
F
F
 
F
F
T
T
F
F
 
F
F
F
T
F

15.
C
D
E
(C v D)
~E
(C v D) ~E
 
T
T
T
T
F
T
T
F
T
T
T
F
T
T
F
T
F
F
T
T
F
T
T
T
F
F
T
F
T
T
F
F
T
F
F
F
F
F
F
T