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0 votes
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Is 1 a lattice?

in Set Theory & Algebra 309 views
1
1) lattice

2) not lattice

3) lattice
0
I think

1) Not lattice  (It's meet semi-lattice)  because there's no LUB for vertex d and g )

2) Lattice

3) Lattice
0
2 cannot be lattice
0

Why  srestha  mam ??

2) have both LUB and GLB 

 

2

@magma  second one is not lattice  b,e  does not have LUB and f,g don't have greatest lower bound 

0

WHY ? @Gurdeep Saini

b,e least upper bound is f,

f,g has a glb as e.

2
for a lattice every pair should have unique GLB and unique LUB but have it is 2
0
ya got it !

2 Answers

1 vote
 
Best answer

In (2) for f & g we don't have greatest lower bound hence not a lattice. 


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0
hey  ,In (f , g) ---->    h is LUB and e is GLB
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see for {b,e}
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(b,e) --- > f is LUB and a is GLB
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chk again it has 2 lub
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yes 2 is not lattice
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Should GLB and LUB of a lattice be unique ?
2 votes

second is not a lattice

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