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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

DM-Groups and Lattice-Q10


Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
+2 votes

image

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 by gbeditor-2 (72,840 points)
reshown Jul 9, 2019 by gbeditor-2

3 Answers

–1 vote
B is correct one
answered Jul 9, 2019 by (34,820 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 (9,500 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 (970 points)
Answer:

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