STQC-NIELIT STA 2021
March 2, 2025ICT
March 3, 2025GATE 2005
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Question 9
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The following is the Hasse diagram of the poset [{a,b,c,d,e},<]
The poset is
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not a lattice
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a lattice but not a distributive lattice
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a distributive lattice but not a Boolean algebra
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a Boolean algebra
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Question 9 Explanation:
It is lattice because both LUB and GLB exist for each pair of the vertex in above Hasse diagram.
But it is not distributed because for some element there are more than one complement. Moreover if it is not distributive then it can’t be boolean.
But it is not distributed because for some element there are more than one complement. Moreover if it is not distributive then it can’t be boolean.
Correct Answer: B
Question 9 Explanation:
It is lattice because both LUB and GLB exist for each pair of the vertex in above Hasse diagram.
But it is not distributed because for some element there are more than one complement. Moreover if it is not distributive then it can’t be boolean.
But it is not distributed because for some element there are more than one complement. Moreover if it is not distributive then it can’t be boolean.