DM-Groups and Lattice-Q10

+2 votes


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 in Discrete Maths by gbeditor (23,750 points)
reshown Jul 9 by gbeditor

3 Answers

0 votes
B is correct one
answered Jul 9 by tsnikhilsharmagate2018 (31,600 points)
+1 vote
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 by tscontactadarshkumar (8,810 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 by prashantpro19 (200 points)