Please prove the following with clear steps and/or related theorems.Problem 2. If X is a set, P(X) denotes the set of all subsets of X. So for example, ifX = {x, y}, then P(X) is the set {Ø, {x}, {y}, {x, y}}. For subsets A and B of X, let A + Bdenote the set of x € X such that r is in both A and B or x is in neither A nor B.(i) Show that (P(X), →,U) is a ring.(ii) For subsets A and B of X, A®B denotes the set of points in X that belong to exactlyone of the sets A and B. Show that (P(X), , n) is isomorphic to (P(X), +,U).(iii) Show that every prime ideal of P(X) is maximal.

As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Please prove the following with clear steps and/or related theorems. Problem 2. If X is a set, P(X) denotes the set of all subsets of X. So for example, if X = {x, y}, then P(X) is the set {Ø, {x}, {y}, {x, y}}. For subsets A and B of X, let A + B denote the set of x € X such that x is in both A and B or æ is in neither A nor B. (i) Show that (P(X), →,U) is a ring.

Please prove the following with clear steps and/or related theorems. Problem 2. If X is a set, P(X) denotes the set of all subsets of X. So for example, if X = {x, y}, then P(X) is the set {Ø, {x}, {y}, {x, y}}. For subsets A and B of X, let A + B denote the set of x € X such that x is in both A and B or æ is in neither A nor B. (i) Show that (P(X), →,U) is a ring.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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