Commutative laws
The commutative laws state that the order of propositions does not affect the truth value of conjunction or disjunction.
Statements
- p ∧ q ≡ q ∧ p
- p ∨ q ≡ q ∨ p
Explanation
The logical value of a conjunction or disjunction remains unchanged when the order of the operands is swapped.
Examples
- "I study AND I pass the exam" is equivalent to "I pass the exam AND I study".
- "It rains OR it snows" is equivalent to "It snows OR it rains".
Truth Table (Conjunction)
| p |
q |
p ∧ q |
q ∧ p
|
| T |
T |
T |
T
|
| T |
F |
F |
F
|
| F |
T |
F |
F
|
| F |
F |
F |
F
|
Truth Table (Disjunction)
| p |
q |
p ∨ q |
q ∨ p
|
| T |
T |
T |
T
|
| T |
F |
T |
T
|
| F |
T |
T |
T
|
| F |
F |
F |
F
|