DM-Groups and Lattice-Q13

+1 vote

Let [N,\leq] is a partial order relation defined on natural numbers. Identify the false statement?

(A). [N,\leq] is distributive but not complemented lattice

(B). [N,\leq] is not a lattice

(C). [N,\leq] is not Boolean lattice

(D). Element 1 doesn't have complement

asked Jul 8, 2019 in Discrete Maths by gbeditor (32,710 points)
reshown Jul 9, 2019 by gbeditor

4 Answers

0 votes
B is correct one
answered Jul 9, 2019 by (34,820 points)
Can you explain why it wont be a lattice? Pick any two elements, they will have a LUB and GLB.
+1 vote
it is example of total order set that is always distributive
answered Jul 10, 2019 by (3,750 points)
But here ask which of the following not correct.
0 votes
The correct answer is B. We have updated it.
answered Jul 11, 2019 by getgatebook (34,850 points)
0 votes
Here, the relation is less than or equal to specifically, right?

and also universal upper bound doesn't exist because natural numbers will go on and on, right? and that's  why it's not complemented lattice, right? please help me, thanks.
answered Jan 2 by rajatmaheshwari2572one (8,000 points)
edited Jan 2 by rajatmaheshwari2572one