Adam & Eve

Imagine a woman who is the most recent female ancestor that you and I share. Let's define this relation as our "grand-eve". If you're Heather (my sister), our "grand-eve" is our mother. Depending on how closely related you are to me, our "grand-eve" might be your grandmother, your great-grandmother, your great-great grandmother, etc...

Now consider the man who is the most recent male ancestor that you and I share. Let's call him our "grand-adam".

Three questions to ponder: Is it necessarily the case that you and I have a grand-eve? Is it necessarily the case that you and I have grand-adam? And finally, if you and I have a grand-eve and a grand-adam, must they have known each other?