I want to ask how to prove question 9? and why proving a subset would be enough if the proof has it. 9. Using the notation of the previous problem, prove that for sets A, B,C, DE P(X)AAB = CAD → AAC = BAD. 8. Given sets A, B E P(X), their symmetric difference is defined byAAB = (A – B) U(B – A) = (AU B) – (An B).

First we take forward part and take an element in A∆C and show that it is in B∆D and then take…

Answered: 9. Using the notation of the previous…

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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Prove the given statements by Direct Proof: “∀?, ? ∈ Z+ − {1}, ?2 | ?2 ↔ ? |?.”
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in how many ways can the numbers 1,2,3,4,5,6,7 be arranged so that a. 1 and 7 are adjacent? b. 1 and 7 are not adjacent? c. 1 and 7 are exactly three spaces apart?
For these proofs I know have to use "subsets" but not sure how I think the 2nd problem may involve a proof with cases. Prove A - B is equivalent to A n Bnot Prove Anot U Bnot is equivalent to Anot n Bnot Prove if A subset B, then AnBnot = null (I think do a proof by contrapositive but not sure how)
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9. Using the notation of the previous problem, prove that for sets A, B, C, DE P(X) AAB = CAD → AAC = BAD. %3|