Consider the relations R(w, x, y, z) and S(a, b). For each of the
following constraints on R, state which of insert/update/delete trigger(s)
are needed, and give a trigger that enforces the constraint (if
multiple triggers are needed, you only need to give one):

1. Primary key is (w,x)

2. y must be unique

3. z must not be null

4. wx -> yz *and* y -> x (BCNF violation)

5. y is a foreign key on S(a) (assume S does not change).

6. For any given (w,z), no change to R may cause the number of
   matching rows to drop below 3.

7. Changes are not allowed to alter a row's primary key in R.

8. Challenger: suppose we have the following view:

create view T as select R.*, S.b from R join S on x=a;

... with R.x a foreign key reference to S.a. Define a trigger that
allows an attempted insert on T to create new rows in R and S, as long
as neither primary key exists yet (in which case the attempt to insert
into a view is well-defined).

In other words, given the data below, attempts to insert T(1,2,3,4,5)
or T(3,4,5,6,7) should fail but T(5,6,7,8,9) should succeed and create
new rows R(5,6,7,8) and S(6,9):

R(w,x,y,z)      S(a,b)
===========     =======
1 2 3 4         2 5
1 4 5 6         4 7