Exercise 2, § 1

Let E be a bigebra such that P(E) = {0} and let (E_n)_{n \geq 0} be a filtration of E compatible with its bigebra structure. Show by induction on n that E_n^+ = {0} for all n \geq 0 and deduce that E^+ = {0}, i.e. that E reduces to K.