This is Theorem 5.2.4 from Durrett's Probability Theory and Examples.
If $X_n$ is a submartingale with respect to $F_n$ and $\phi$ is an increasing convex function with $E|\phi(X_n)|<\infty$ for all $n$, then $\phi(X_n)$ is a submartingale with respect to $F_n$. Consequently (i) If $X_n$ is a submartingale, then $(X_n-a)^+$ is a submartingale. (ii) If $X_n$ is a supermartingale, then $X_n\wedge a$ is a supermartingale.
I don't understand how to get (ii) from the theorem. I think I should consider $-X_n$, thus getting a submartingale, but I can't think of a convex function, which after putting $-$ back I would get $X_n\wedge a$. I would greatly appreciate any help.