"Some teachers are not sincere" is an example of which category of proposition?

A categorical proposition is classified along two independent dimensions: its quantity — universal ('All ...' / 'No ...') versus particular ('Some ...') — and its quality — affirmative versus negative. Traditional logic names the four resulting combinations A, E, I, and O.

The given sentence, ‘Some teachers are not sincere,’ opens with the quantifier ‘some’ rather than ‘all’ or ‘no,’ and its predicate ‘sincere’ is denied by ‘not.’ Matching quantity to the Particular row and quality to the Negative row places the sentence in the O row of the table above.

• vs. ‘No teachers are sincere’ (Universal negative): that phrasing would claim something about every teacher; the given sentence's opening word restricts the claim to only part of the group, so a 'universal' label overstates it.

• vs. ‘All teachers are sincere’ (Universal affirmative): that reading both broadens the quantifier and removes the denial, a double change to the original sentence.

• vs. ‘Some teachers are sincere’ (Particular affirmative): that phrasing keeps the same quantifier but drops the word 'not,' turning a denial into an assertion.

Since the sentence combines a particular quantifier with a negative predicate, it is the O-form — Particular Negative — proposition.