Principle of distributivity

The principle of distributivity states that the algebraic distributive law is valid, where both logical conjunction and logical disjunction are distributive over each other. == In Propositional Logic == For any propositions A, B and C, the following equivalences hold: A ∧ ( B ∨ C ) ⟺ ( A ∧ B ) ∨ ( A ∧ C ) {\displaystyle A\land (B\lor C)\iff (A\land B)\lor (A\land C)} A ∨ ( B ∧ C ) ⟺ ( A ∨ B ) ∧ ( A ∨ C ) {\displaystyle A\lor (B\land C)\iff (A\lor B)\land (A\lor C)} === Proof using truth tables === The distributive laws can be verified using truth tables.

Source: Wikipedia — Principle of distributivity (CC BY-SA 4.0)

Principle of distributivity

The principle of distributivity states that the algebraic distributive law is valid, where both logical conjunction and logical disjunction are distributive over each other. == In Propositional Logic == For any propositions A, B and C, the following equivalences hold: A ∧ ( B ∨ C ) ⟺ ( A ∧ B ) ∨ ( A ∧ C ) {\displaystyle A\land (B\lor C)\iff (A\land B)\lor (A\land C)} A ∨ ( B ∧ C ) ⟺ ( A ∨ B ) ∧ ( A ∨ C ) {\displaystyle A\lor (B\land C)\iff (A\lor B)\land (A\lor C)} === Proof using truth tables === The distributive laws can be verified using truth tables.

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Source: Wikipedia "Principle of distributivity" · CC BY-SA 4.0

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