A broadcast network is a classical network with all source messages collocated
at a single source node. For broadcast networks, the standard cut-set bounds,
which are known to be loose in general, are closely related to union as a
specific set operation to combine the basic cuts of the network. This paper
provides a new set of network coding bounds for general broadcast networks.
These bounds combine the basic cuts of the network via a variety of set
operations (not just the union) and are established only via the submodularity
of Shannon entropy. The tightness of these bounds are demonstrated via
applications to combination networks.