Excuse the very basic question:
I'm following Milnor's Lectures on Characteristic Classes. He defines a relation on the collection of compact, smooth, oriented manifolds of dimension $n$ by letting $M_1\sim M_2$ if $M_1\sqcup -M_2$ is a boundary (If $M$ is a manifold, then $-M$ is the same manifold with the opposite orientation). He uses this to define cobordism classes and further goes on to define a graded ring structure on these classes. He says clearly the relation is reflexive and symmetric. I see symmetric, but I'm not entirely sure why this relation is reflexive. Since we're supposed to have a group structure, and the $0$ element is the empty set, I'm assuming that the boundary of $M\sqcup -M$ is the empty set. Why is it that $\partial (M\sqcup -M)=\emptyset $ ? Do the two manifolds somehow cancel each other out since they have opposite orientations? How can I picture this?