Question 1089563



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