Can we determine FDs if we are given some tuples?
No. The reason why database designers are interested in FDs is because they are a formalisation of Business Rules - rules about the data which accurately reflect the Business Domain to be modelled in the database. The only sound and practical way to identify FDs is by analysing and understanding a set of business requirements.

Suppose you are designing a database for a members-only club and you are given the data for all current members. You notice that for every member Sex = "Male". Can you conclude from the data that the club only admits men? Of course not. The only way to know that is by knowing what the club rules are. You could conclude from the data that the club is not a women-only club, but that's something different. Knowing what dependencies do not apply isn't the same as knowing what dependencies do apply.

You can of course use data to help you test a set of given FDs (by making sure that the FD holds for every row of some sample data) but you first have to know what FDs to try; you shouldn't expect to derive them from data alone.