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In this paper, we first present an outer bound for a general interference channel with a cognitive relay, i.e., a relay that has non-causal knowledge of both independent messages transmitted in the interference channel. This outer bound reduces to the capacity region of the deterministic broadcast channel and of the deterministic cognitive interference channel the through nulling of certain channel inputs. It does not, however, reduce to that of certain deterministic interference channels for which capacity is known. As such, we subsequently tighten the bound for channels whose outputs satisfy an “invertibility” condition. This second outer bound now reduces to the capacity of the special class of deterministic interference channels for which capacity is known. The second outer bound is further tightened for the high-SNR deterministic approximation of the Gaussian channel by exploiting the special structure of the interference. We provide an example that suggests that this third bound is tight in at least some parameter regimes for the high-SNR deterministic approximation of the Gaussian channel. Another example shows that the third bound is capacity in the special case where there are no direct links between the non-cognitive transmitters.