In this article , you will find common laws for preposition logic. These are very helpful in solving problems like simplifying a complex prepositional statement into a simple one. They also form the basis for arguments which you will learn in future lessons.
Identity Laws (1)
| p | T | p and T |
|---|---|---|
| 0 | 1 | 0 |
| 1 | 1 | 1 |
| p | F | p or T |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 0 | 1 |
Domination Laws (2)
| p | T | p or T |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 1 | 1 |
| p | F | p and F |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 0 | 0 |
Idempotent Laws (3)
| p | p | p or p |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| p | p | p and p |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
Double Negation Law (4)
| p | not p | not (not p) |
|---|---|---|
| 0 | 1 | 0 |
| 1 | 0 | 1 |
Commutative Laws (5)
| p | q | p or q | q or p |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 |
| p | q | p and q | q and p |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
Associative Laws (6)
| p | q | r | p or q | q or r | (p or q) or r | p or (q or r) |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Distributive Laws (7)
| p | q | r | q and r | p or (q and r) | p or q | p or r | (p or q) and (p or r) |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
De Morgan’s Laws (8)
| p | q | not p | not q | not(p or q) | not p and not q |
|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| p | q | not p | not q | not(p and q) | not p or not q |
|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 1 |
Absorption Laws (9)
| p | q | p and q | p or (p and q) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 |
| p | q | p or q | p and (p or q) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 |
Negation Laws (10)
| p | not p | p or not p |
|---|---|---|
| 0 | 1 | T |
| 1 | 0 | T |
| p | not p | p and not p |
|---|---|---|
| 0 | 1 | F |
| 1 | 0 | F |