Let $Θ(G)$ 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 $Θ(G\sqcup H)>Θ(G)+Θ(H)$ and $Θ(G\boxtimes H)>Θ(G)Θ(H)$. This was shown independently by Wigderson and Zuiddam [2022] using Kadison-Dubois duality and the Axiom of choice.
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