Six Cities Puzzle | Logic Puzzle

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There are six cities A,B,C,D,E and F
A is not a hill station.
B and E are not historical places.
D is not an industrial city.
A and D are not historical cities.
A and B are not alike.
Assuming that there are 2 cities of each type :
Hill Station, Historical City and Industrial Town,
Which two cities seem to be Industrial Centres ?

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Answer is A and E
Logic :
Since B,E,A,D are not Historical Cities
Therefore C and F are Historical Cities
A is also not a Hill Station
So A is one of the Industrial Centre.
Since A and B are not alike. B is not and Industrial Centre. B is a Hill Station.
D is not an Industrial City, hence D is also a Hill Station.
This leaves us with E as an Industrial Centre.
Hence A and E are Industrial Centres.
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