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It is a partially ordered set (P, ≤) in which any two elements  P has single GLB and single LUB.


In the Fig. (a) GLB and LUB are shown, which are also called meet and join respectively.


The poset shown in Fig. (c) is not a lattice since a and b have two LUBs namely c and d.

From first lattice, following relations are obtained :

1 ≤ 2, 1 ≤ 3, 2 ≤ 4 and 3 ≤ 4.

Here 2 and 3 are not compared.

If (P, ≤ ) is a lattice, then (P, ≥ ) is also a lattice, we define as
≥ follows

(x ≤ y)  y ≥ x.

In other words, GLB and LUB are interchanged if we interchange relations ≤ and ≥.

In terms of lattices, operations of meet and join on (L, ≤) become the operations of join and meet on (L, ≤).

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