I found an interesting handout outlining the problem of induction and the possible solutions. It is inconclusive as is the problem, but it will help you think about the assignment on the scientific method & induction. I have put it up temporarily at this location.
Now about the replies to the assignment. Saarang, Ockham's razor is not opposite to inductive reasoning, and it only says that given a choice between possible explainations, choose the one with least inductive thinking OR in other words the one with minimum assumptions.
Shivang, I agree with (1), but about Ockham and GR & QM ... We cant see the future and so we have to limit ourselves to making the bext of what we have today. A theory when made has to deal with every known aspect of the phenomenon. That's the criterion. If there are some variants of the phenomena that we have not yet encountered or any parameters that we haven't considered which do not affect the observed phenomena, then that cannot question the veracity of the theory. GR and QM were never designed to work for the microscopic and the fast, respectively. But then there is Relativistic QM which ensures that the rules of the Relativity are applied to QM objects. We haven't yet corrcetly integrated QM with gravity, but that would be another theory altogether, based on diffirent assumptions and evolving its own different principles.
Anyways keep the answers coming guys...the problem is still out there...