Answered: Let X be a set and define the binary…

Let X be a set and define the binary operation ∆ on the subsets of X by A∆B := (A∩Bc)∪(B∩Ac). Prove that the set P(X) of all subsets of X is a group under the operation ∆.

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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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

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Let X be a set and define the binary operation ∆ on the subsets of X by A∆B := (A∩B^c)∪(B∩A^c).

Prove that the set P(X) of all subsets of X is a group under the operation ∆.

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