DM-Groups and Lattice-Q10

+2 votes

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Which of the above hasse diagrams (a),(b),(c) is/are is lattice? 

(A).Only (a)

(B).Only (a) and (c)

(C).Only (b) and (c) 

(D).All of (a),(b) and (c)

asked Jul 8, 2019 in Discrete Maths by gbeditor (24,360 points)
reshown Jul 9, 2019 by gbeditor

3 Answers

0 votes
B is correct one
answered Jul 9, 2019 by tsnikhilsharmagate2018 (34,740 points)
+2 votes
for a hasse diagram to be lattice every pair of element must have unique LUB and GLB.

in diagram b

LUB(b,c)= d or e            GLB(d,e)=b,c

so diagram b is not lattice
answered Jul 9, 2019 by tscontactadarshkumar (9,200 points)
Yes This type of diagram called cross structure poset
0 votes
It should be B.

But the diagram C is wrong . Since poset is a set , how can elements repeat?
answered Oct 5, 2019 by prashantpro19 (200 points)
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