# whether given lattice is distributive or complemented or both?

whether given lattice is distributive or complemented or both?

       a
/|\
/ | \
b  |  c
|  d  |
e  |  f
\  | /
\ |/
g


For a lattice to be distributive each element should have unique complement. here d can have two b & c , hence it is not distributive. Am I right?

You are correct. Another way to see this (which might be easier for more complicated lattices) is to note that the lattice has $N_5$ and $M_3$ as sublattices. A lattice is distributive iff it has no sublattice isomorphic to $N_5$ or $M_3$. (A lattice is modular iff it has no sublattice $\cong N_5$.)