Tenant moving early, return part of rent?

[Aaron Johnston]

I just closed on my first rental properties and served a tenant a 30 day notice to vacate the unit by July 1. Notice was served in May. My question is since they paid for the month of June but they are moving out half way through the 30 days, should I prorate their rent and give some of it back? I tried looking for an answer in forums but had no luck.