And we will prove the properties of lattices. Together we will learn how to identify extremal elements such as maximal, minimal, upper, and lower bounds, as well as how to find the least upper bound (LUB) and greatest lower bound (GLB) for various posets, and how to determine whether a partial ordering is a lattice. Boolean Lattice – a complemented distributive lattice, such as the power set with the subset relation.Īdditionally, lattice structures have a striking resemblance to propositional logic laws because a lattice consists of two binary operations, join and meet.The study of lattices is called lattice theory. Distributive Lattice – if for all elements in the poset the distributive property holds. An algebra is called a lattice if is a nonempty set, and are binary operations on, both and are idempotent, commutative, and associative, and they satisfy the absorption law. Namely, the complement of 1 is 0, and the complement of 0 is 1.
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