re-screen exisiting tenants when buying?

[Eric Geurkink]

I have an offer accepted on a duplex - first property.  Tenants are month to month and a little under market. So I wanted to keep them both and gradually move up if they were good. One had their power turned off during the inspection. So that one's out. I still have to get rental payment history on the other, am told that its fine, but I'll be raising rent a bit. What are the guidelines to serving one notice to vacate but keeping the other? Does there have to be "Cause"? I'm in MN.  We are closing too late to have a notice vacant prior to closing. 

Thanks for any tips!