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Lattice

 

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

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

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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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