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Which of the following is/are true:

  1. In distributive lattice; complements are unique?
  2. All complemented lattices are distributive?
  3. All distributive lattices are complemented?

According to me-

for complemented lattice – each element must have atleast 1 complement

for distributive lattice – each element may have atmost 1 complement

so 3 is wrong.

and 2 is true?

what about 1?
answer is only 1 is right. HOW?

in Mathematical Logic by (26 points) | 25 views

3 Answers

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In Distributive lattice, if a complement exist it must be unique. Hence, 1 is true.

All complemented lattice is not distributive, because in complemented lattice an element can have more than 1 complement. Therefore 2 is also False.

I don’t get it you have the right logic. Then why are getting confused?
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Ya got confused for no reason:|
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