Controlled airspace is the airspace where services of air traffic control are provided.  There are different classifications of controlled airspace. Class A airspace is one of the categories of controlled airspace. In Class, A airspace Instrument Flight Rules, authorized operations are the only ones permitted to use it. In Class A category of airspace, all the flights are separated from each other. Also, for Class B airspace, air traffic control services are provided. However, Class B airspace the flights permitted to use it are the Instrument Flight Rules flights and Visual Flight Rules. Class B airspace mainly involves the airspace that is within the biggest airports. Also, all the flights are separated from each other in the Class B airspace category. learn more here

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Instrument Flight Rules flights and Visual Flight Rules flights are also allowed for Class C airspace. Class C airspace flights have air traffic control services given. Airports using Class C airspace usually have an operational control tower.  The aircraft using Class C airspace need to have a two way radio communication with an air traffic control facility before using the airspace. The communication, once established, should be kept on till the flight leaves the airspace. Class C airspace allows Instrument Flight Rules Visual Flight Rules. However, Class C airspace category usually separate flights of Instrument Flight Rules from each other and Visual Flight Rules. Flights of Visual Flight Rules are usually separated from Instrument Flight Rules. Read more here

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Class D airspace permits both Instrument Flight Rules flights and Visual Flight Rules flights. Flights in the Class D airspace category are also provided with air traffic control services. Communication between an aircraft air traffic control facility is also similar to that of Class C airspace where a two way radio communication with air traffic control facility before using the airspace and while within the airspace is set up and maintained. Also, flights using Instrument Flight Rules flights are separated from each other, and the information relayed to them is usually concerning Visual Flight Rules flights. However, Visual Flight Rules flights get information concerning all the other classification of flights. 

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There is the Class E airspace. Class C airspace is any other airspace that is not classified but is controlled airspace. Class C airspace category is the one that makes up the largest controlled airspace. In Class E airspace Instrument Flight Rules flights and Visual Flight Rules flights are also allowed.

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More details https://www.youtube.com/watch?v=9TIBeso4abU