If I hadn't set the morning alarm, I would be late to class.
I wasn't late to class.
Had I set the alarm?
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A ⟹ B is equivalent to n o t B ⟹ n o t A
A l a r m − n o t − s e t ⟹ L a t e − t o − c l a s s is equivalent to N o t − l a t e − t o − c l a s s ⟹ A l a r m − s e t