New Account/Cable Hookup

I recently purchased the Cox Internet panoramic wifi setup. I moved into an apartment that is connected to my landlords residence and they use Verizon as a subscriber. I did not wish to use their wifi anymore and wanted to go to a different service provider as to not interfere with their services. In looking at the cable hookup, I realized that I may not be able to connect to my tv as the tv is connected to Verizon. Can I connect my cable from the new Cox modem/router to my tv. Nothing was said in the verbiage that I had to have Cox cable network established, all I want is to be able to have my own internet and wifi. Can someone please advise, thank you.