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+7 votes
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The Hasse diagrams of all the lattices with up to four elements are _____ (write all the relevant Hasse diagrams)
asked in Set Theory & Algebra by Veteran (59.6k points) | 659 views
0

Anything other than this?

+1
one more is straight line ryt ?
+1
Chain diagram;

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

This might help ...

3 Answers

+17 votes
Best answer
1. Diamond structure
2. Straight line structure
answered by Veteran (55.6k points)
selected by
0
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 

answered by Loyal (7.6k points)
0
Why can't we draw a lattice with one element ?
0
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--->4....in vertical manner.
answered by Loyal (9.1k points)

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