SQL provides an n-ary operation called coalesce, which is defined as follows: coalesce(A1, A2,..., An) returns the first nonnull Ai in the list A1, A2,..., An, and returns null if all of A1, A2,..., An are null.

Let a and b be relations with the schemas A(name, address, title), and B(name, address, salary), respectively. Show how to express a natural full outer join b using the full outer-join operation with an on condition and the coalesce operation. Make sure that the result relation does not contain two copies of the attributes name and address, and that the solution is correct even if some tuples in a and b have null values for attributes name or address.