P0002_Soln - P0002_Soln.doc A) A ( =) ( B ( P − AB )( )...

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Unformatted text preview: P0002_Soln.doc A) A ( =) ( B ( P − AB )( ) Prove that P∪ P + BP∩ First, introduce some convenient new notation… X Y Z A B In this new notation, we see that… P ) P ) P) AXY ( =( +( P) P) P) BY Z ( =( +( P ∩ = () A) Y ( BP P∪ P)P + Z A) X Y ( = ( B ( +( P) ) So, start with new notation… P∪ P)P + Z A) X Y ( = ( B ( +( P) ) Then add and subtract P(Y) from RHS … P∪ P +Y P +Y P A) X ( =) ( B ( P +Z P −Y )( ( ( ))) Groups RHS so that can see relationship with original notation… P∪ (X P ) P + Y P A ) ( + Y (Z () Y = −) ( B P) ( + ( P) ( ) ) Substitute back into original notation… P∪ P + BP∩ A) A ( =) ( B ( P − AB )( ) ...
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