Let $X$ be a locally Noetherian scheme without embedded point, show that $X$ is reduced if and only if it is reduced at the generic points.
Let $X$ be a locally Noetherian scheme (maybe has some embedded points), do we have $X$ is reduced if and only if it is reduced at the associated points?
Question (1) is from Liu Qing's book "Algebraic Geometry and Arithmetic Curves" exercise 7.1.2. If possible, I want to see a global proof, do not reduced to the affine scheme please. I guess there are some geometric meanings, maybe you can help me to point it.