# Thread: Finding Sublattice for a given Lattice

1. ## Finding Sublattice for a given Lattice

In the first part I have to find $L1$ as a sublattice of $L2$, so i am assuming that no sides can probably be added in $L2$ in which case i can't find $L1$ in $L2$.
Need some help here .

Also in the second part, I know that I probably have to find two shaded dots that $join$ or $meet$ at the unshaded dot, but I can't find such a pair. Am I thinking along the right lines or is there some other way of doing the second part ?

2. ## Re: Finding Sublattice for a given Lattice

If $L_1$ is a sublattice of $L_2$, it does not mean that the Hasse diagram of $L_1$ is a subgraph of the Hasse diagram of $L_2$. The order in a lattice is transitive, so you can connect two elements in a sublattice that were not connected in the lattice. I believe you can take $c$ or $e$ as the rightmost element of $L_1$.

Concerning (ii), according to Wikipedia, a sublattice is not a subset that is a lattice, but a subset that is closed under the original meet and join operations. Since there are two shaded elements whose join in the sense of $L_3$ is not shaded, the shaded elements don't form a sublattice.

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# how can i know lattice has sublattice or not

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