  Let $\Theta(G)$ denote the Shannon capacity of a graph $G$. We give an
elementary proof of the equivalence, for any graphs $G$ and $H$, of the
inequalities $\Theta(G\sqcup H)>\Theta(G)+\Theta(H)$ and $\Theta(G\boxtimes
H)>\Theta(G)\Theta(H)$. This was shown independently by Wigderson and Zuiddam
[2022] using Kadison-Dubois duality and the Axiom of choice.
