The student's question pertains to set theory and the intersection of the complement of set D with set E. However, there's a mix-up with a physics reference regarding particle numbers in energy intervals. The correct mathematical interpretation of D^{c} n E is not related to the physics formula provided.
The notation D^{c} n E represents the intersection of the complement of the set D with the set E in mathematics. Essentially, it is the set of all elements that are in E but not in D. The expression you've provided seems to be a typo or an error, as the TeX formatting should not be included when asking about set operations. Moreover, the given reference is related to the number of particles with a specific energy in physics and does not seem to be relevant to your question.
If instead, you need assistance with understanding how to determine the number of particles dN with energies in a narrow energy interval, which can be expressed by dN = n(E) dE = g(E) dE · F, the equation represents the differential number of particles in that energy interval. The function n(E) is generally the density of states, g(E) is the energy state degeneracy, and F could represent the Fermi-Dirac distribution (for fermions) or the Bose-Einstein distribution (for bosons), depending on the context.