This problem is associated with a collection of connected subsets

Problem 7.4. Prove the following stronger variant of Proposition 7.4. Suppose C is collection of connected subsets of a. metric space X and B E C. Show, if for each A E C, A n B 7 (D, then P : U{C : C E C} is connected. [Suggestionz Consider the collection D = {C U B 2 C' E C}