Question

1.34 Let A. A.. be a countable collection of subsets of U.Prove the following. a) If B cU, An, then B U,(An n B). b) If Un An-U, then E U(An E) for each subset E of U c) If Ai, A2,... are pairwise disjoint, so are Ain E, A2n E,... for each subset E of U d) We say that Ai, A2,... form a partition of U if they are pairwise disjoint and their union is U. Conclude from parts (b) and (c) that, if Ai, A2. form a partition of U, each subset E of U can be expressed as a disjoint union of the sets Ai n E, A2nE,

Part(c) and partd(d)

Answer 1