# Distributive Operation Relation

(Redirected from distributive property)

A Distributive Operation Relation is an equality relation between two arithmetic operations of that is based on the distributive law.

## References

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Distributivity
• In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra. For example:
• 2 x (1 + 3) = (2 x 1) + (2 x 3).
• In the left-hand side of the above 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 results added afterwards. Because these give the same f==Definition==
• Given a set S and two binary operations · and + on S, we say that the operation ·
• is left-distributive over + if, given any elements x, y, and z of S: x · (y + z) = (x · y) + (x · z);
• is right-distributive over + if, given any elements x, y, and z of S: (y + z) · x = (y · x) + (z · x);
• is distributive over + if it is both left- and right-distributive. [1]
• Notice that when · is commutative, then the three above conditions are logically equivalent.