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The following is the Hasse diagram of the poset [{a,b,c,d,e},≺]

The poset is :

1. not a lattice
2. a lattice but not a distributive lattice
3. a distributive lattice but not a Boolean algebra
4. a Boolean algebra
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if any subset contains above structures, then it is not a distributive lattice.

we know given hasse diagram is lattice and it containing above structue so it is not distributive. B

Option b ,a lattice has lub and glb but to be distributive it should have unique complement.
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Yes it is a lattice should have unambiguous unique suprenum and infinum for all horizontal elements in the hasse diagram.
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How to calculate complement can any1 plz explain.

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shubhamdarokar try checking whether LHS and RHS are same in  $b \wedge (c \vee d)=(b\wedge c)\vee(b\wedge d)$. If yes, it is a distributive lattice, else not.

Option B is appropriate for it.

It is lattice bcz both LUB and GLB exist for each pair of the vertex in above Hasse diagram.

But It not Distributed bcz there exist more than complement of element.So it ever be Boolean algebra.

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@Paras Nath given Hasse diagram is totally different from poset  i think given reation is not '<' (less than ) it is other relation defined according to hasse diagram

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yes, it may be any relation. because nothing is mentioned about it. But, this can be answered by looking at hasse diagram only.