Neutral and dominance laws
Jump to navigation
Jump to search
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 |