"(For simplicity, you should not introduce projections over attributes other than those attributes already projected.)"
Isn't it true that in almost every case when pushing a projection, the new projection must include more attributes than the original one (for example, when pushing the projection through a natural join, the new projection must include the join attributes)? In this case, it seems none of the projections in the assignment can be pushed without introducing new attributes. Well, we were just trying to make the problem easier. Normally, yes, you have to introduce additional attributes in projections. For this assignment, just push projections down as far as you can without adding attributes. You should find that even without introducing attributes, projections can be pushed down, especially once you push the selections down.