An operator on relations is said to be monotone if whenever we add a tuple to one of its arguments, the result contains all the tuples that it contained before adding the tuple, plus perhaps more tuples. Which of the following operators are monotone? For each, either explain why it is monotone or give an example showing it is not. 1. Union 2. Intersection 3. Difference 4. Cross Product 5. Natural Join 6. Theta Join 7. Selection 8. Projection