GATE IT 2008 | Question: 28

Question

Consider the following Hasse diagrams.

1. 
2. 
3. 
4. 

 

Which all of the above represent a lattice?

• A. (i) and (iv) only
• B. (ii) and (iii) only
• C. (iii) only
• D. (i), (ii) and (iv) only

Comments

yess , not distributive

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i think for (ii) since it has more than one minimal element so it cannot be a lattice

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no need to check 3rd eliminated from the option cuz 1 st one was correct.

Answer 1

 We can visualize (ii) as shown in image. 2 minimal elements so directly we can say it is not a lattice. Check image for other details.

And fig. 2 and 3 neither meet nor join semiLattice. So, answer is A)

Also Thanks other members for good discussion.

Answer 2

See in diagram (ii) for non-comparable elements there is no first "unique" meeting point i.e. no unique GLB. So it is not a lattice. Similarly in diagram (iii) for the upper side  non- comparable elements there is no first unique meeting point i.e. GLB and for the lower side non-comparable elements there is no first "unique " joining point i.e. LUB. That's why Option A is the correct answer.

Answer 3

Hasse diagram is lattice when every pair of elements have a LUB and a GLB.

In figures (ii) and (iii), every element is not having a least upper bound and a greatest lower bound. So false

Answer 4

For element b, d

GLB (b, d) = (c. e) but GLB must be unique i.e. only 1 element present in GLB. Hence not lattice.

So, (ii) and (iii) are not lattice