What is a man and what is a woman...

I really struggled with this question, because every time I come up with a definition I find exceptions.  I would like to say that in general a man has a penis and a woman has a vagina, but I find that there are so many exceptions to this rule that I almost reject that definition entirely.  I do agree that many of our perceptions about what it means to be a man or a woman are simply social constructions which we follow in order to relate to the people around us.  I even remember thinking as a kid that as a white person with ambiguous roots in America, I didn't really have any culture or group to relate to except for women and feminists.  Now of course I find myself relating to individuals, or humanity as a whole more so than my gender.  I do believe that men and women should be equal, and I'm finding it more and more difficult every day to really see the differences between them.