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Math Help - Finding Sublattice for a given Lattice

  1. #1
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    Question 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 Finding Sublattice for a given Lattice-img03335-20140503-1726.jpgthinking along the right lines or is there some other way of doing the second part ?
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  2. #2
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    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.
    Thanks from mrmaaza123
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