**Distributive Property**

In abstract algebra and logic, **distributivity** is a property of binary operations that generalizes the **distributive law** from elementary algebra. In propositional logic, **distribution** refers to two valid rules of replacement. The rules allow one to reformulate conjunctions and disjunctions within logical proofs.

For example, in arithmetic:

- 2 × (1 + 3) = (2 × 1) + (2 × 3) but 2 /(1 + 3) is not equal to (2 / 1) + (2 / 3).

In the left-hand side of the first equation, the 2 multiplies the sum of 1 and 3; on the right-hand side, it multiplies the 1 and the 3 individually, with the products added afterwards. Because these give the same final answer (8), we say that multiplication by 2 *distributes* over addition of 1 and 3. Since we could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, we say that multiplication of real numbers *distributes* over addition of real numbers.

Read more about Distributive Property: Definition, Propositional Logic, Examples, Distributivity and Rounding, Distributivity in Rings, Generalizations of Distributivity

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