Students are asked to prove the following statement: Theorem: If An B = AUB, then P(AŬB) = P(A). One student provides the following proof: Proof: Let A,B be sets such that AnB = AUB. Let x (AUB). Sox CAUB by the definition of power sets. So x An B by our assumption. So In particular CA by specialization. Thus, x ≤ P(A) by the definition of power sets. Thus, P(A) = P(AUB). A and B by the definition of intersection. Is the student's proof correct? If the student is correct, then fill in the needed to • make the proof completely correct • make sure each assertion made is fully justified • make the proof written in such a way that a student in the class could follow the logic and be fully convinced that the theorem is true. If the student is incorrect, then Identify any errors in the proof above. Explain each error. Your explanation should be written to the student who made the error, and should try to help the student understand why what they wrote is incorrect. ●

Students are asked to prove the following statement: Theorem: If An B = AUB, then P(AŬB) = P(A). One student provides the following proof: Proof: Let A,B be sets such that AnB = AUB. Let x (AUB). Sox CAUB by the definition of power sets. So x An B by our assumption. So In particular CA by specialization. Thus, x ≤ P(A) by the definition of power sets. Thus, P(A) = P(AUB). A and B by the definition of intersection. Is the student's proof correct? If the student is correct, then fill in the needed to • make the proof completely correct • make sure each assertion made is fully justified • make the proof written in such a way that a student in the class could follow the logic and be fully convinced that the theorem is true. If the student is incorrect, then Identify any errors in the proof above. Explain each error. Your explanation should be written to the student who made the error, and should try to help the student understand why what they wrote is incorrect. ●

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...

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