Simplify the given expression. Cite a property from each expression     A − (A ∩ B)   ∩ B − (A ∩ B)   =  A ∩ (A ∩ B)c  ∩ B ∩ (A ∩ B)c   = A ∩ (A ∩ B)c ∩ B ∩ (A ∩ B)c   = A ∩ (A ∩ B)c ∩ B  ∩ (A ∩ B)c = A ∩ B ∩ (A ∩ B)c  ∩ (A ∩ B)c = A ∩ B ∩ (A ∩ B)c ∩ (A ∩ B)c   = A ∩ B ∩ (A ∩ B)c    = (A ∩ B) ∩ (A ∩ B)c  = ∅

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Simplify the given expression. Cite a property from each expression 

  

A − (A ∩ B)   ∩ B − (A ∩ B)

 

A ∩ (A ∩ B) ∩ B ∩ (A ∩ B)c

 

= A ∩ (A ∩ B)c ∩ B ∩ (A ∩ B)c

 

= A ∩ (A ∩ B)c ∩ B  ∩ (A ∩ B)c

= A ∩ B ∩ (A ∩ B)c  ∩ (A ∩ B)c



= A ∩ B ∩ (A ∩ B)c ∩ (A ∩ B)c

 

= A ∩ B ∩ (A ∩ B)c

   = (A ∩ B) ∩ (A ∩ B)c

 = ∅

 

 

 

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