May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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8-16 Discrete Mathematical Structures
Example 5 Let A = {2, 3, 4, 6} be a poset with ≤ being the divisibility relation. It is not a lattice
since sup{4, 6} = LCM(4, 6) = 12 does not belong to A.
Example 6 Find whether the following posets shown in Fig. 8.19b given below are lattices.
3
4
2
5
1
Figure 8.19(a)
e
d
f
c
a
b
Figure 8.19( b)
Solution:
(a) is a lattice as supremum and infimum of every pair of elements exists.
(b) is not a lattice as infimum of (a, b) does not exist. Similarly, supremum of (e, f ) does not
exist.
8.12 LATTICE IN TERMS OF ALGEBRAIC STRUCTURES
A non-empty set L closed under binary operations ∧ and ∨ is called a lattice (L, ∧, ...
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