- No student goes to school today.
- No students go to school today.
When and why do I have to use singular and plural nouns following "No"?
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I would say that the difference runs thus (based on my usage):
A plural form would be used for a collective decision or to stress a collective situation. No students go to school today implies that school has been cancelled for all students; perhaps it was a snow day or merely a weekend.
A singular form would be used for a collection of independent decisions, most often as the basis for personal action, or to stress an individual choice or mandate. No student goes to school today implies that each student has made the independent choice not to go to school today; I would most often see why should I? tacked onto the end of it.