Truth Tables on Two Propositions
|
p |
q |
t |
Ú |
¬ |
p |
® |
q |
« |
Ù |
Ø (pÙ q) |
Å |
Ø q |
Ø (p® q) |
Ø p |
Ø (q® p) |
Ø (pÚ q) |
c |
|
T |
T |
T |
T |
T |
T |
T |
T |
T |
T |
F |
F |
F |
F |
F |
F |
F |
F |
|
T |
F |
T |
T |
T |
T |
F |
F |
F |
F |
T |
T |
T |
T |
F |
F |
F |
F |
|
F |
T |
T |
T |
F |
F |
T |
T |
F |
F |
T |
T |
F |
F |
T |
T |
F |
F |
|
F |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
|
col. # |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
|
Are these 16 all the possible distinct operators on two propositions?
To answer this question we make a possibility tree. First recall that there are four rows in any truth table on two propositions, and each row can be one of only two values, T or F. Thus there are two distinct choices for the first row; for each of these choices there are two choices for a second row (22 = 4 possible combinations); for each of these there are two choices for a third row (22× 2 = 8); and then there are two choices for the fourth row. All together there are 24 = 16 possible combinations of T and F (truth tables) on two propositions.
Truth Tables on Two Propositions
|
p |
q' |
p' |
pq |
pq |
(pq)' |
p |
q' |
pq' |
p' |
p'q |
(p+q)' |
||||||
|
p |
q |
t |
Ú |
¬ |
p |
® |
q |
« |
Ù |
Ø (pÙ q) |
Å |
Ø q |
Ø (p® q) |
Ø p |
Ø (q® p) |
Ø (pÚ q) |
c |
|
T |
T |
T |
T |
T |
T |
T |
T |
T |
T |
F |
F |
F |
F |
F |
F |
F |
F |
|
T |
F |
T |
T |
T |
T |
F |
F |
F |
F |
T |
T |
T |
T |
F |
F |
F |
F |
|
F |
T |
T |
T |
F |
F |
T |
T |
F |
F |
T |
T |
F |
F |
T |
T |
F |
F |
|
F |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
|
col. # |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
|