Did my ex-boyfriend cheat on me if he started a new relationship while we were separated but living in the same house?

Anonymous
My ex-boyfriend and I share an 8-year-old child. Although we were never married, we lived together until recently when he moved out due to starting a new relationship. He ended our relationship, citing that I wasn't treating him well, and I was reluctant to attend therapy, leading him to give up. We separated two years ago, but I requested him to continue staying in the house to help with our child. He agreed but opted to sleep in a different bedroom.

Despite attempting to reconcile shortly after the separation, he made it explicitly clear that our relationship was over, and there was no chance of reconciliation. After that, we had minimal communication for two years, only discussing matters related to our son during occasional weekend face to face chats. Although we separated, we never discussed dating other people, and truthfully, I didn't anticipate him dating someone else. Did he cheat on me?
Did my ex-boyfriend cheat on me if he started a new relationship while we were separated but living in the same house?
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