logic: contraries

two propositions are said to be contrary if the cannot both be true. that is the truth of one entails the falsity of the other.

they can both be false

All poets are dreamers (A)
No poets are dreamers(E)

A&E propositions having the same subject and predicate terms are contraries.

propositions that are neither necessarily true nor necessarily false are said to be contigent.

for example the following propositions:

all squares are rectangles
no squares are circles

each represents a mathematical truth and therefore cannot have a contrary.