grammaticality - Singular or plural "set"?


I'm having some issues with a sentence that is part of the purpose in a report that I'm writing. I'm not sure if the word "communicate" (in bold) should be singular or plural.


The applications in the "set" will communicate with each other, not with other "sets".



The purpose of this report is to develop a sample set of applications that communicates between services on the internet, mobile devices and a central processing unit in a motor vehicle.





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