Just a quick one (Sets and Relations)

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SUMMARY

The discussion centers on set theory, specifically the manipulation of set operations involving differences and unions. The user presents a series of equations involving sets A and B, ultimately demonstrating that the expression (A ∩ B) - (A ∪ B) simplifies to (A ∩ B) - (B ∪ A). The conversation emphasizes the importance of understanding theorems related to set operations and their implications in mathematical proofs.

PREREQUISITES
  • Understanding of basic set theory concepts, including unions and intersections.
  • Familiarity with set notation and operations.
  • Knowledge of theorems related to set differences and complements.
  • Ability to manipulate algebraic expressions involving sets.
NEXT STEPS
  • Study the properties of set operations in detail, focusing on De Morgan's laws.
  • Learn about theorems related to set differences and their applications.
  • Explore advanced topics in set theory, such as cardinality and infinite sets.
  • Practice solving problems involving complex set expressions and proofs.
USEFUL FOR

Mathematicians, students studying discrete mathematics, and anyone interested in deepening their understanding of set theory and its applications in logic and proofs.

Natasha1
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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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