§ Example of lattice that is not distributive

• Take a 2D vector space, and take the lattice of subspaces of the vector space.
• Take three subspaces; a = x, b = y, c = x + y.
• Then see that c /\ (a \/ b) = c, while c /\ a = c /\ b = 0, so (c /\ a) \/ (c /\ b) = 0.