Relation between Lattice and Boolean Algebra

In discrete math, I have read that lattice is a generalized form of boolean lattice. But those places where boolean algebra is mentioned, they don't tell about lattices (digital logic, binary,...). Whether the meet and join is same as and and or in boolean logic? If we are thinking in terms of lattices how you define 1 and 0 = 0? We consider only a two element lattice?

• – D.W. Oct 12 '16 at 4:52

A better description would be to say that boolean algebra forms an extremely simple lattice. It has two elements, $\top$ and $\bot$, with $\bot \sqsubset \top$. The meet corresponds to conjunction (AND), and the join corresponds to disjunction (OR), though you can make a dual lattice with these flipped.