secretary of education has 1 distinct synonym spread across 2 of its 2 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the person who holds the secretaryship of the Department of Education
“Carter appointed Shirley Hufstedler as the first Secretary of Education”
the position of the head of the Education Department
“the post of Education Secretary was created in 1979”
Synonyms, antonyms and the broader and narrower relations for secretary of education come from Princeton University’s WordNet. Full sources and licences.