In the case of the umbrellas and the rain, the deductive method might or might not be more effective than an empirical investigation. The empirical method of going outside and extending an upturned palm has the advantage of rendering you safe from most false premises. The advantage of the deductive method in this case is that you do not have to go outside and get wet to obtain an answer. We constantly use deduction to help us deal with the world. And off you go to class on the basis of your deduction, without telephoning to check that classes are indeed meeting.
Deduction is particularly useful for improving our understanding of the world in two situations.
The first is where we believe we know the logic of some phenomenon, but have little information about it. Thus, scientists deduced much knowledge about nuclear fission from other knowledge about physics, long before they were able to run actual fission experiments. When we have more than two premises, or when the premises are more complex, or when the relationships among the premises are more complex, the deductions are not so obvious. Sophisticated logical analysis can then help us draw conclusions. Until recent decades many people considered logic an arid subject, useless for practical purposes.