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MATH SOLVE
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Show that (A | B) U (B \ A) = (AUB) \(B n A).
4 months ago
Q:
Show that (A | B) U (B \ A) = (AUB) \(B n A).
Accepted Solution
A:
Answer:We have to prove,(A \ B) βͺ ( B \ A ) = (A U B) \ (B β© A).Suppose,x β (A \ B) βͺ ( B \ A ), where x is an arbitrary,β x β A \ B or x β B \ Aβ x β A and x β B or x β B and x β Aβ Β x β A or x β B and x β B and x β Aβ x β A βͺ B and x β B β© Aβ x β ( A βͺ B ) \ ( B β© A )Conversely,Suppose,y β ( A βͺ B ) \ ( B β© A ), where, y is an arbitrary.β y β A βͺ B and x β B β© Aβ y β A or y β B and y β B or y β Aβ Β y β A and y β B or y β B and y β Aβ Β y β A \ B Β or Β y β B \ A β Β y β ( A \ B ) βͺ ( B \ A )Hence, proved......