The following is the Hasse diagram of the poset [{a, b, c, d, e}, ≤] The poset…
2005
The following is the Hasse diagram of the poset [{a, b, c, d, e}, ≤]
The poset is
- A.
not a lattice
- B.
a lattice but not a distributive lattice
- C.
a distributive lattice but not a Boolean algebra
- D.
a Boolean algebra
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Show answer & explanation
Correct answer: B
it is lattice since join and meet exists for every pair of elements .
but not a distributed lattice as for distributive lattice every element must have 0 or at most 1 complement , here b,c,d have multiple complement .
hence option B is correct
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