# What is chain in lattice?

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Definition 2.3 Each ordered subset of

**lattice**is known as one of its**chains**. If a**chain**of**lattice**is not included in any other**chains**, then the**chain**is defined as a maximum**chain**.

Similarly, it is asked, what is lattice with example?

For **example**, the set {0, ½, 1} with its usual ordering is a bounded **lattice**, and ½ does not have a complement. A bounded **lattice** for which every element has a complement is called a complemented **lattice**. A complemented **lattice** that is also distributive is a Boolean algebra.

**chain**is a totally ordered subset of a poset S; an

**antichain**is a subset of a poset S in which any two distinct elements are incomparable. A maximal

**chain**(

**antichain**) is one that is not a proper subset of another

**chain**(

**antichain**).

In this manner, what is lattice in Hasse diagram?

**Lattices** – A Poset in which every pair of elements has both, a least upper bound and a greatest. lower bound is called a **lattice**. There are two binary operations defined for **lattices** – Join – The join of two elements is their least upper bound.

Noun. **bounded lattice** (plural **bounded lattices**) (algebra, order theory) Any **lattice** (type of partially ordered set) that has both a greatest and a least element.