State and verify absorption law in boolean algebra
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the absorption law or absorption identity is an identity linking a pair of binary operations.
Two binary operations, ¤ and ⁂, are said to be connected by the absorption law if:
a + (a • b) = a • (a + b) = a.
A set equipped with two commutative, associative and idempotent binary operations ∨ ("join") and ∧ ("meet") that are connected by the absorption law is called a lattice.
The absorption law does not hold in many other algebraic structures, such as commutative rings, e.g. the field of real numbers, relevance logics, linear logics, and substructural logics. In the last case, there is no one-to-one correspondence between the free variables of the defining pair of identities.
Two binary operations, ¤ and ⁂, are said to be connected by the absorption law if:
a + (a • b) = a • (a + b) = a.
A set equipped with two commutative, associative and idempotent binary operations ∨ ("join") and ∧ ("meet") that are connected by the absorption law is called a lattice.
The absorption law does not hold in many other algebraic structures, such as commutative rings, e.g. the field of real numbers, relevance logics, linear logics, and substructural logics. In the last case, there is no one-to-one correspondence between the free variables of the defining pair of identities.
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