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In this paper our recent results in the capacity of single relay erasure channels are used to derive a new and tighter cut-set bound. We initially present a simple and intuitive approach to derive the classical cut-set bound in General Multi-Terminal Erasure Channels. This derivation shows that attaining the bound supposes that a full level of collaboration exists between nodes in the channel. However under some scenarios the full collaboration is not possible. We thereafter use a bounding technique based on reducing every cut-set in a General Multi-Terminal Erasure Channel to a single relay super-channel consisting of super nodes. We show that if a rate setting is not achievable over the single relay super-channel it could not then achieved over the General Multi-Terminal Erasure Channel. This led us to a tighter cut-set type of bound for General Multi- Terminal Erasure Channel.