Distributive Law

A Distributive Law is a replacement rule between two set operations or arithmetic operations that is based on the corresponding Boolean algebra law.

• Context
  • It is based on following Boolean algebra distributive laws:
    • Distributivity of [math]\displaystyle{ \vee }[/math] over [math]\displaystyle{ \wedge }[/math]: [math]\displaystyle{ p \vee (q \wedge r) \equiv (p \vee q) \wedge (p \vee r) }[/math]
    • Distributivity of [math]\displaystyle{ \wedge }[/math] over [math]\displaystyle{ \vee }[/math]: [math]\displaystyle{ p \wedge (q \vee r) \equiv (p \wedge q) \vee (p \wedge r) }[/math]
• Example(s):
  • Set Distributive Law,
  • Multiplication Distributive Law,
  • Division Distributive Law,
  • Distributive Lattice.
• Counter-Example(s)
  • Commutative Law.
  • Associative Law.
• See: De Morgan's Laws, Equality Relation, Binary Operation, Distributive Operation Relation.

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