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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 ⋅ (1 + 3) = (2 ⋅ 1) + (2 ⋅ 3), but 2 / (1 + 3) ≠ (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), it is said that multiplication by 2 ''distributes'' over addition of 1 and 3. Since one 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. ==Definition== Given a set and two binary operators ∗ and + on , we say that the operation: ∗ is ''left-distributive'' over + if, given any elements , and of , :: ∗ is ''right-distributive'' over + if, given any elements , and of , :: and ∗ is ''distributive'' over + if it is left- and right-distributive.〔Ayres, (p. 20 )〕 Notice that when ∗ is commutative, the three conditions above are logically equivalent. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Distributive property」の詳細全文を読む スポンサード リンク
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