Not sure if this question has been asked before, but anyways. I was wondering if someone wouldn't mind clarifying what the question is asking:
"Among the examples above, the inclusion maps are one-to-one, but, except in some trivial special cases, the projection are not. Exercise: What special cases?" -Halmos Section 8 Pg. 32
Just as background, he presents the the projection functions onto $X$ and $Y$ from $X \times Y$, and the canonical map; sorry, it is really a lot to write, but there is an online copy pg.32.
What I am most confused about is the inclusion map for the (seemly ambiguous) "projection". What I am thinking is $i: P \times Q \rightarrow X \times Y$, $P \subset X$ and $Q \subset Y$. However, the only way I could see this failing 1-1 is in cases $P \times Q = \emptyset$, yet I am not sure if that is what this question is asking.
EDIT: One of my biggest questions is if $i$ as stated above is indeed the "projection" inclusion map. It seems like it is not the projection.
Any help would be appreciated.