Logical Identities
Cards (14)
- Logical identities are fundamental principles or equivalences that hold a truth value of true in logic.
- Logical identities it is used to simplify and manipulate logical expressions.
- Identity Laws
- p ∧ True = p
- p ∨ False = p
- Domination Laws
- p ∧ False = False
- p ∨ True = True
- Idempotent Laws
- p ∧ p = p
- p ∨ p = p
- Commutative Laws
- p ∧ q = q ∧ p
- p ∨ q = q ∨ p
- Associative Laws
- (p ∧ q) ∧ r = p ∧ (q ∧ r)
- (p ∨ q) ∨r=p∨(q∨r)
- Distributive Laws
- p ∧ (q ∨ r) = (p ∧ q) ∨ (p ∧ r)
- p ∨ (q ∧ r) = (p ∨ q) ∧ (p ∨ r)
- Complement / Inverse Laws
- p ∧ ¬p = False (Contradiction Law)
- p ∨ ¬p = True (Excluded Middle Law)
- De Morgan's Laws
- ¬(p ∧ q) = ¬p ∨ ¬q
- ¬(p ∨ q) = ¬p ∧ ¬q
- Absorption Laws
- p ∨ (p ∧ q) = p
- p ∧ (p ∨ q) = p
- Double Negation Law
- ¬(¬p) = p
- Implication
- p → q = ¬p ∨ q
- Equivalence
- p<->q = (p→q) ∧ (q→p)