Question $12$

$(2)$

This is about the Hasse Diagrams of partially ordered sets shown above.

Select one of the following choices:

a$.(1)$ and $(2)$ are lattices, but $(3)$ is not a lattice

b$.(1),(2),$ and $(3)$ are not lattices

c$.$ None of the Given Choices

d$.(1),(2),$ and $(3)$ are lattices

e$.(1)$ and $(3)$ are lattices, but $(2)$ is not a lattice

f$.(2)$ and $(3)$ are lattices, but $(1)$ is not a lattice