contrary

nouns

a relation of direct opposition
"we thought Sue was older than Bill but just the reverse was true"
exact opposition
"public opinion to the contrary he is not guilty"
is a type of (narrower)
the relation between opposed entities
a logical relation such that two propositions are contraries if both cannot be true but both can be false
is a type of (narrower)
a relation between propositions

adjectives

very opposed in nature or character or purpose
"acts contrary to our code of ethics"; "the facts point to a contrary conclusion"
is similar to
unlike in nature or quality or form or degree
"took different approaches to the problem"; "came to a different conclusion"; "different parts of the country"; "on different sides of the issue"; "this meeting was different from the earlier one"
of words or propositions so related that both cannot be true but both may be false
"`hot' and `cold' are contrary terms"
is similar to
of words: having opposite meanings
resistant to guidance or discipline
"Mary Mary quite contrary"; "an obstinate child with a violent temper"; "a perverse mood"; "wayward behavior"
is derived from
in an opposing direction
"adverse currents"; "a contrary wind"