SOLUTION: (A union B)=(A union C) & (A intersection B)=(A intersection C) then PROVE THAT B=C

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Question 1089563: (A union B)=(A union C) & (A intersection B)=(A intersection C) then PROVE THAT B=C
Answer by MathLover1(20849) About Me  (Show Source):
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given:
(A U B) =(A U C)
(A ∩ B)=(A ∩ C)
proof:
(A U B) =(A U C)
=>(A U B)∩ C =(A U C) ∩ C
=>(A ∩ C) U (B∩ C) = C.........(distributive law)
=>(A U B) = A U C
=>(A U B)∩ B = (A U C) ∩ B
=>B = (A∩ B) U (C∩ B).........(distributive law)
=>B = (A∩ C) U (C∩ B)................[given (A∩ B)=(A∩ C) ]
=>B = C