The determining factor is when did the term end? If the published school term ended in Apr then May will not count. If the published term ended in May then it does count.
Graduation date is not a factor; there may be only one sometimes two grad dates per year for a school and many students will actually have finished months earlier.
Yes, you are correct on the rules for determining the eligibility for the refundable part of the AOC and the full-time student status test for dependency testing.
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