Distributive property
In abstract algebra and formal logic, the
distributive property of binary operations 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 · = +, but 2 / ≠ +. 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, 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.