Need help with this math problem. I received feedback from my Professor for this homework problem and he said Connex? I think he meant connex relation. Below the homework problem is my work. 1.2:121. Let A be a nonempty set. Let ~ be a relation on(A) defined by:Letting B and C be arbitrary subsets of A, B-C iffBCC.Proof..What kind of order is (if any)? Prove the propertiesthat hold, and construct counterexamples for theproperties that don't.LTEA is given to be a non-empty set of 2 and ~ is therelation on (A) that is defined byB and C be arbitrary subsets of A,B-C iff BCCSince B~B. BCBB-B V BE(A)is a Reflexive relation<(Every set is a subset of itself)Let B,C and D be any three subsets of (A) of BCC and CCB⇒ B=C ⇒ relation (B~C iff BCC)> 2:14A is given torelation on (A) that is defined byB and C be arbitrary subsets of A,B-C iff BCC.. is a Reflexive relationSince B~B. BCB (Every set is a subset of itself)B~BV BE(A)~⇒ B=C ⇒ relation (B~C iff BCC)~ is Anti-SymmetricLet B,C and D be any three subsets of (A) of BCC and CCBNow let B-C ⇒ BCCC~D⇒ CCDSince BCCCD ⇒ BCDLTEand is the⇒B~D<⇒ is TransitiveThus, relation '~' and partial ordering on (A)

Answered: Image /qna-images/answer/de2958ed-c218-438d-b569-40d518930961.jpg

1. Let A be a nonempty set. Let ~ be a relation on (A) defined by: Letting B and C be arbitrary subsets of A, B-C iff BCC. What kind of order is~ (if any)? Prove the properties that hold, and construct counterexamples for the properties that don't.

1. Let A be a nonempty set. Let ~ be a relation on (A) defined by: Letting B and C be arbitrary subsets of A, B-C iff BCC. What kind of order is~ (if any)? Prove the properties that hold, and construct counterexamples for the properties that don't.

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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