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6. Let U be a set and let X be the power set of U (that is, the set of all subsets of U). Consider the operation of symmetric difference of sets, defined by AAB = (AU B) – (An B) = (A – B)U (B – A). The operation of symmetric difference is a binary operation on X. a) Show that A is commutative. b) Is there an identity element? c) Does every set A have an inverse? What is it? d) Is (U, A) a group?

6. Let U be a set and let X be the power set of U (that is, the set of all subsets of U). Consider the operation of symmetric difference of sets, defined by AAB = (AU B) – (An B) = (A – B)U (B – A). The operation of symmetric difference is a binary operation on X. a) Show that A is commutative. b) Is there an identity element? c) Does every set A have an inverse? What is it? d) Is (U, A) a group?

Advanced Engineering Mathematics
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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6. Let U be a set and let X be the power set of U (that is, the set of all subsets of U). Consider the operation of symmetric difference of sets, defined by AAB = (AU B) – (AN B) = (A – B)U (B – A). - - The operation of symmetric difference is a binary operation on X. a) Show that A is commutative. b) Is there an identity element? c) Does every set A have an inverse? What is it? d) Is (U, A) a group?
Transcribed Image Text:6. Let U be a set and let X be the power set of U (that is, the set of all subsets of U). Consider the operation of symmetric difference of sets, defined by AAB = (AU B) – (AN B) = (A – B)U (B – A). - - The operation of symmetric difference is a binary operation on X. a) Show that A is commutative. b) Is there an identity element? c) Does every set A have an inverse? What is it? d) Is (U, A) a group?
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