Introduction to Logic

Truth-Tables V

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

1.
A
B
~A
~A B
~B
A ~B
~ (A~B)
A B
 
T
T
F
F
F
T
T
T
F
F
F
T
T
F
F
 
F
T
T
F
F
T
T
F
F
T
F
T
F
T
T
 

2.
A
B
~B
A ~B
~(A ~B)
A B
 
T
F
F
T
T
T
F
T
T
F
F
 
T
F
T
F
T
F
F
T
T
F
T
 

3.
F
G
 H
F G
~ H
(F G) ~H
 
T
  T
F
F
1
2
T
T
T
T

1
2

T
F
F
F
T
T
F
T
T
1
2
F
T
T
F
F
T
 
F
F
T
T
1
2
F
F
T
F
F
T
 
F
F
F
T
T

4.

A
B
~A
~A B
~B
A ~B
~ (A~B)
A B
 
T
T
F
F
F
T
T
T
F
F
T
T
F
F
F
T
T
T
F
F
T
T
 
F
F
T
T
F
T
T


5.
A
B
~B
A ~B
~(A ~B)
A B
 
T
T
F
T
T
T
F
T
F
F
F
T
T
F
T
F
F
T
F
T

6.
F
G
 H
F G
~ H
(F G) ~H
 
T
T
T
 
F
F
T
T
F
T
T
T
F
T
F
T
T
F
F
T
T
F
T
T
F
F
T
 
F
T
F
F
T
T
 
F
F
T
F
T
F
F
F
F
T
T
 

7.

A
B
~A
~A B
~B
A ~B
~ (A~B)
A B
 
T
T
F
F
F
T
T
T
F
F
F
T
F
F
F
T
T
T
F
F
T
T
 
F
F
T
F
F
T
T

8.
A
B
~B
A ~B
~(A ~B)
A B
 
T
T
F
T
T
T
F
T
F
F
F
T
F
T
F
T
 
F
F
T
T
F
T
 

9.
F
G
 H
F G
~ H
(F G) ~H
 
T
T
T
  T
F
T
T
F
T
T
T
F
T
F
T
T
F
F
F
T
F
T
T
F
F
T
 
F
T
F
F
T
T
 
F
F
T
F
F
T
 
F
F
F
F
T
T
 

10.
A
B
~A
~A B
~B
A ~B
~ (A~B)
A B
 
T
T
F
F
F
T
T
T
F
F
F
T
F
F
 
F
T
T
T
F
T
T
F
F
T
F
T
T
T
 

11.
A
B
~B
A ~B
~(A ~B)
A B
 
T
T
F
F
T
T
 
T
F
T
T
F
F
 
F
T
F
F
T
F
F
T
F
T

12.
F
G
 H
F G
~ H
(F G) ~H
 
T
T
T
  T
F
T
T
F
T
T
T
F
T
F
F
T
F
F
F
T
T
 
F
T
T
F
F
T
 
F
T
F
F
T
T
 
F
F
T
F
F
T
 
F
F
F
F
T
T
 

13.
A
B
~A
~A B
~B
A ~B
~ (A~B)
A B
 
T
T
F
F
F
F
T
T
F
F
F
T
T
F
 
F
T
T
T
F
F
T
 
F
F
T
F
T
F
T

14.
A
B
~B
A ~B
~(A ~B)
A B
 
T
T
F
F
T
T
F
T
T
F
F
T
F
T
T
F
F
T
T
T

15.
F
G
 H
F G
~ H
(F G) ~H
 
T
T
T
  T
F
F
 
T
T
F
T
T
T
 
T
F
T
F
F
T
 
T
F
F
F
T
T
 
F
T
T
F
F
T
 
F
T
F
F
T
F
F
T
F
F
F
F
F
F
T

 

16.

A
B
~A
~A B
~B
A ~B
~ (A~B)
A B
 
T
T
F
F
F
F
T
T
F
F
F
T
T
F
F
T
T
T
F
F
T
F
F
T
F
T
F
T

17.

A
B
~B
A ~B
~(A ~B)
A B
 
T
T
F
F
T
T
F
T
T
F
F
T
F
T
F
F
F
T
T
F

18.

F
G
 H
F G
~ H
(F G) ~H
 
T
T
T
  T
F
F
 
T
T
F
T
T
T
 
T
F
T
F
F
T
 
T
F
F
F
T
F
T
T
F
F
F
T
F
F
T
T
 
F
F
T
F
F
T
 
F
F
F
F
T
T