Just a quick one (Sets and Relations)

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The discussion revolves around verifying a set theory equation involving set differences and unions. The user seeks confirmation on the correctness of their derivation and requests explanations of the theorems applied at each step. Key transformations include the use of set identities and properties, such as the intersection and union of sets. The final expression simplifies to a relationship between the intersection and union of sets A and B. The inquiry highlights the importance of understanding foundational set theory concepts.
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Can anyone just check if I got it right please?
And if so could you just explain the theorems that come with each line? Many many thanks in advance :smile:

(A-B) n (B-A) = (AuB’) n (BuA’)
= (Au(BuA’)) u(B’n (BuA’))
= ((AnB) u (AnA’)) u ((B’nB) u (B’nA’))
= (AnB) u Ø u Ø u (B’nA’)
= (AnB) u (B’nA’)
= (AnB) u (BuA)’
= (AnB) - (BuA)
= (AnB) - (AuB)
 
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