Idempotent laws

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