Should I be honest when someone ask which part of the paper is mine? Not sure if this is an obvious question, or if someone has asked this. If so please tell me.

Suppose I and A have a (math) paper. There are two parts, and I believe the first part is done by me, and the second part is done by A.

Now someone asked me a few questions.


Is first part your part/ your work?
Is second part your part/ your work?


Easy to see I have a few options here.

a. That is my part.

b. That is not my part.

c. That is our joint work.

I suppose, if I claim my part to be my part, I should not claim A's part as my part or our joint work. And claiming my part to be my part will also lead to a problem when we have another author B who doesn't really has his part. That is, probably we worked together and he didn't produce a part. If I claim my part, I might have to end up claiming B doesn't have a part, which doesn't seem to be good.

So the question is, how should I answer such question, when people ask me which part is mine? Also sorry for the bad presentation of the question, and any edits are welcome.
In perspective of contribution, there are only the three options already mentioned by you


the part in question is based only on work you did, or
the part in question is based on work others did, or 
the part in question is based partially on work you contributed to.


In each case I would tell this frankly.  Seeing the publication as the whole thing, prior to submission, everybody who contributed substantially will read again the paper.  This is the then last (of hopefully many earlier) exchanges among the contributors to discus and to clarify why methods were applied this way, and not an other. So that everyone among the contributors sees intent and purpose of the publication, the way the "the journey is told", and the conclusions eventually drawn. (consent)

Some publications even include a little section, explicitly stating these contributions, in lines like "Jon Doe designed the experiment, Bob performed the experiment, Jane Doe performed the data analysis, Jon and Abigail P.I. equally contributed writing the paper." *) While I saw such in natural sciences with interdisciplinary work, I see no reason why such would not be possible in mathematics, too.

In an ideal world, should you happen to become the author of correspondence, you should either know every aspect of the paper, or (second best) easily know how to refer to the contributor in question.  This is indeed not a light responsibility supervisors / P.I.s have, especially taking into account the fluctuation of co-workers. (Keyword reproducible research).

*) See, as first example I come to fetch right now, page 16 of Hellinger et al. "The Flashlight Fish Anomalops katoptron Uses Bioluminescent Light to Detect Prey in the Dark" in PLOS one, http://dx.doi.org/10.1371/journal.pone.0170489, section "Author Contributions".