The relation E0 = mc2 is essential to the operation of a power plant based on nuclear fission but has only a negligible relevance for a fossil-fuel plant. Is this a true statement? Explain why or why not.

Yes, this is a true statement.
In nuclear fission, the heavy nuclei of certain substances like uranium may form fission fragments. The total rest mass of these fragments is less than the mass of original heavy nucleus. The difference in the rest mass Δm appears in the form of equivalent energy ΔE = Δm. c² according to the mass energy relation. The liberation of enormous energy due to the decrease in the mass is the basic principle of atom bomb. But in the case of fossil fuel plant, the difference in rest mass Δm is negligible results that there is no liberation of energy. That is why the relation E₀ = mc² is essential to the operation of a power plant based on nuclear fission but has only a negligible relevance for a fossil-fuel plant.