is it necessary that all copolymers undergo addition polymerisation?

Dear Student,

No, all copolymers do not undergo addition polymerisation only. Some undergo condensation polymerisation also. 
Addition polymerisation is the joining of two or more monomers to form a new compound of same empirical formula called polymers. It occurs only when the monomer molecule is unsaturated i.e. it contains double or triple bond. Eg. polythene is formed by addition reaction of ethene monomers. 

Condensation polymerisation occurs when the monomer molecules of different compounds combine with the loss of simple molecules like H2O, HCl, etc. Eg. nylon is formed by condensation polymerisation of adipic acid and hexamethylene diamine.

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