Category: 12. Ordered Sets & Lattices

A complemented distributive lattice is known as a Boolean Algebra. It is denoted by (B, ∧,∨,’,0,1), where B is a set on which two binary operations ∧ (*) and ∨(+) and a unary operation (complement) are defined. Here 0 and 1 are two distinct elements of B. Since (B,∧,∨) is a complemented distributive lattice, therefore…

Let L be a non-empty set closed under two binary operations called meet and join, denoted by ∧ and ∨. Then L is called a lattice if the following axioms hold where a, b, c are elements in L: 1) Commutative Law: –(a) a ∧ b = b ∧ a          …

It is a useful tool, which completely describes the associated partial order. Therefore, it is also called an ordering diagram. It is very easy to convert a directed graph of a relation on a set A to an equivalent Hasse diagram. Therefore, while drawing a Hasse diagram following points must be remembered. The Hasse diagram…

Consider a relation R on a set S satisfying the following properties: Then R is called a partial order relation, and the set S together with partial order is called a partially order set or POSET and is denoted by (S, ≤). Example: Elements of POSET: Note: There can be more than one maximal or…