Given two binary operations and acting on a set , we say that has the distributive property over (or distributes over ) if, for all we have and .
Also note that there is no particular reason that distributivity should be one-way, as it is with conventional multiplication and addition. For example, the set operations union () and intersection () distribute over each other: for any sets we have and .
(In fact, this is a special case of a more general setting: in a distributive lattice, each of the operations meet and join distributes over the other. Meet and join correspond to union and intersection when the lattice is a boolean lattice.)
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