Two closed oriented $n-1$ dimenisonal manifolds $A,B$ are cobordant if there is a compact $n$ dimensional manifold $M$ such that $A \sqcup -B$ diffeomorphic(orientation-preserving) to boundry of $M$.
If there is a diffeomorphism between $A$ and $B$ , can we conclude that $A,B$ are cobordant? Intuitively, I think it is true, but I have trouble to prove this claim.