- 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, whilec /\ a = c /\ b = 0, so(c /\ a) \/ (c /\ b) = 0.
a = x, b = y, c = x + y. c /\ (a \/ b) = c, while c /\ a = c /\ b = 0, so (c /\ a) \/ (c /\ b) = 0.