Absorption laws
The absorption laws show how certain combinations of conjunction and disjunction can be simplified by "absorbing" one proposition into another.
Statements
- p ∨ (p ∧ q) ≡ p
- p ∧ (p ∨ q) ≡ p
Explanation
Adding extra conditions that are already implied by p does not change the truth value.
These laws allow expressions to be reduced in complexity.
Examples
- "I study OR (I study AND I rest)" is logically equivalent to "I study".
- "I study AND (I study OR I rest)" is logically equivalent to "I study".
Truth Table (First Law)
| p |
q |
p ∧ q |
p ∨ (p ∧ q)
|
| T |
T |
T |
T
|
| T |
F |
F |
T
|
| F |
T |
F |
F
|
| F |
F |
F |
F
|
Truth Table (Second Law)
| p |
q |
p ∨ q |
p ∧ (p ∨ q)
|
| T |
T |
T |
T
|
| T |
F |
T |
T
|
| F |
T |
T |
F
|
| F |
F |
F |
F
|