“Zayd is not present” is negative but concerns a determinate individual; it is a negative singular proposition, not a universal negative.
“Some people are travelling” is affirmative but applies only to some; it is a particular affirmative, not a universal affirmative.
“No teacher is absent” denies absence of all teachers. Where negation and a negative-sounding predicate interact, first identify the predicate and the exact scope of the denial.
Evaluating quantity and quality separately makes the classification of the four quantified forms more reliable.