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+8 votes
The Hasse diagrams of all the lattices with up to four elements are _____ (write all the relevant Hasse diagrams)
in Set Theory & Algebra by Veteran (52.1k points) | 871 views

Anything other than this?

one more is straight line ryt ?
Chain diagram;

Like 1-->2--->3---> vertical manner.
what is meant by ' up to 4 elements ' here..should we consider lattices with 3 elements and 2 elements also??

3 Answers

+18 votes
Best answer
1. Diamond structure
2. Straight line structure
by Veteran (60k points)
selected by
For straight line structure one of the relationship could be $cardinality$.

$|\phi| \leq |a| \leq |b| \leq |a,b|$
+3 votes

We cant draw a lattice with 1 element 

by Loyal (7.5k points)
Why can't we draw a lattice with one element ?
i think definition itself says  every pair has lub and glb so atleast 2 element should be there for pair
0 votes
One diamond diagram as u can see above and one like below

Chain diagram;

Like 1-->2--->3---> vertical manner.
by Loyal (9.7k points)

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