Distributive Property - Definition

Definition

Given a set S and two binary operators · 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 left- and right-distributive.

Notice that when · is commutative, then the three above conditions are logically equivalent.

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