# All Science Fair Projects

## Science Fair Project Encyclopedia for Schools!

 Search    Browse    Forum  Coach    Links    Editor    Help    Tell-a-Friend    Encyclopedia    Dictionary

# Science Fair Project Encyclopedia

For information on any area of science that interests you,
enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.).
Or else, you can start by choosing any of the categories below.

# Absorption law

In algebra, the absorption law is an identity between two binary operations, say \$ and %. It is valid and fundamental in Boolean algebra, and lattice theory.

The absorption law states that

a \$ (a % b) = a % (a \$ b) = a.

The interest arises because of the cases where \$ and % are meet and join in order theory. There it is easy to see that the law should hold. In particular, for the binary operators ∧ and ∨, which are defined respectively as the logical AND and OR, the following applies:

a ∧ (ab) = a ∨ (ab) = a.

where = is understood to be logical equivalence over formulae.

Since Boolean algebras are the general form of models for classical logic, and Heyting algebras for intuitionistic logic, the absorption rule also expresses logical equivalences between those logics. Note, however, in the domain of substructural logic, the absorption rule, since it is not linear (there being no 1-1 correspondence between the free variables of the two equations), it does not express logical equivalences in linear logic, nor does it in relevance logic.

03-10-2013 05:06:04