Serre's criterion says that for a scheme to be normal is equivalent to it being $R_1$ (i.e. regular in codimension $1$) and $S_2$ (i.e. regular functions on $X-Y$ extend to $Y$ if $Y$ has codimension at least $2$).

What would be examples of:

- a scheme which is $R_1$, but not $S_2$ (i.e. not normal)?
- a scheme which is $S_2$, but not $R_1$ (i.e. not normal)?