My live in partner cheated me four times, with my cousin we live in one roof,what should I do?should I forgive him?

You're dilusional even considering forgiving him. If you do, what makes you think he won't do it again? Now that he knows he can and get away with it.

No. Forgiving him would imply that he thinks there's something he needs forgiven for. But cheating four times means he doesn't care if it hurts you and wouldn't care about your forgiveness. Unless you're happy being 1 of X number of women, leave him.