May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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8-22 Discrete Mathematical Structures
2. D
30
= {1, 2, 3, 5, 6, 10, 15, 30} is a complemented lattice as each element has a
complement.
3. The lattice P(∪) of all subsets of a universal set ∪ is complemented lattices as each subset
A ∈ ∪ has the unique complement.
4. The lattice whose diagram is given below is a complemented lattice.
1
0
5. The lattice whose diagram is given below
1
0
a
b
c
is a complemented lattice.
8.19 CHAIN AND ANTICHAIN
Let (A, ≤ ) be a poset. A subset of A is called a chain, if every two elements in the subset are
related.
d
c
b
a
e
Figure 8.22
In Fig. 8.22 {a, b, c, d}, {a, b, c}, {a, e, d} and {a} are chains.
If A itself is a chain, ...
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