Absorption laws
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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 |