Commutative laws
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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 |