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In this, the second part of a two-part paper, we apply the result of Part I  to three problems in multi-user communication. 1) For the special case of the broadcast channel where both channels are binary symmetric, we establish a converse result that shows the ad hoc scheme suggested by Cover and Bergmans , [3l is in fact optimal. 2) For a modified version of a source coding problem with side information of Slepian and Wolf , we establish a converse result. 3) We show that the "common information" of a certain pair of dependent random variables is zero.