Test Series

Question

Is 1 a lattice?

Comments

1) lattice

2) not lattice

3) lattice

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I think

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

2) Lattice

3) Lattice

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2 cannot be lattice

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Why  srestha  mam ??

2) have both LUB and GLB 

 

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

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WHY ? @Gurdeep Saini

b,e least upper bound is f,

f,g has a glb as e.

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for a lattice every pair should have unique GLB and unique LUB but have it is 2

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ya got it !

Answer 1

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

Comments

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 ?

Answer 2

second is not a lattice