Idempotent laws
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Idempotent laws
The idempotent laws state that combining a proposition with itself using either conjunction or disjunction does not change its truth value.
Statements
- p ∧ p ≡ p
- p ∨ p ≡ p
Explanation
A proposition combined with itself is logically equivalent to the proposition alone.
Examples
- "I study AND I study" is logically the same as "I study".
- "I study OR I study" is also logically the same as "I study".
Truth Table (Conjunction)
| p | p ∧ p |
|---|---|
| T | T |
| F | F |
Truth Table (Disjunction)
| p | p ∨ p |
|---|---|
| T | T |
| F | F |