logic: contraditories

two propositions are contradictory if one is the denial or the negation fo the other. they cannot both be true and they cannot both be false.

i think it means if one is true the other can not possibly be true. so, if all cars are dogs. the contradictory of that would be some cars are not dogs.

• must differ from one another in quantity
• must differ from one another in quality

from the text

all judges are lawyers (A proposition)
some judges are not lawyers? (O proposition)

no politicians are idealists (E)
some politicians are idealists (I)

of the pair, exactly one is true and exactly one is false. they cannot both be true and cannot both be false.

A&O propositions are contradictories
E&I propositions are contradictories