Part 1: Let A be a set. Define a relation on as follows:For B and C arbitrary subsets of A, B~C iff B\C =empty set . If this is an equivalence relation, select the response that indicates as much. If this is not an equivalence relation, select all of the properties that the relation fails. Part 2: Let A be a set. Define a relation on as follows:Letting B and C be arbitrary subsets of A, then B~C iff B intersect C not= empty set. If ~ is an equivalence relation, select the answer that indicates as much. If ~ is not an equivalence relation, select all of the properties of an equivalence relation that are failed. Let A be a set. Define a relation on p (A) as follows:For B and C arbitrary subsets of A, B~C iff B\C = Ø. If this is an equivalence relation, select theresponse that indicates as much. If this is not an equivalence relation, select all of the properties thatthe relation fails.O SymmetricIt is an equivalence relation.ReflexiveO TransitiveQuestion 75 ptsLet A be a set. Define a relation on p (A) as follows:Letting B and C be arbitrary subsets of A, then B~C iff B N C Ø. If ~ is an equivalence relation,select the answer that indicates as much. If ~ is not an equivalence relation, select all of theproperties of an equivalence relation that are failed.O No answer text provided.O SymmetricO TransitiveO TrueO Reflexivity

Answered: Image /qna-images/answer/29b7708c-80e4-4d3d-b446-fcafe54f8b28.jpg

Answered: Let A be a set. Define a relation on p…

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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Part 1: Let A be a set. Define a relation on as follows:
For B and C arbitrary subsets of A, B~C iff B\C =empty set . If this is an equivalence relation, select the response that indicates as much. If this is not an equivalence relation, select all of the properties that the relation fails.

Part 2: Let A be a set. Define a relation on as follows:
Letting B and C be arbitrary subsets of A, then B~C iff B intersect C not= empty set. If ~ is an equivalence relation, select the answer that indicates as much. If ~ is not an equivalence relation, select all of the properties of an equivalence relation that are failed.