contrary

In an opposing direction.

“a contrary wind”

Resistant to guidance or discipline.

“Mary Mary quite contrary”

Of words or propositions so related that both cannot be true but both may be false.

“`hot' and `cold' are contrary terms”

Very opposed in nature or character or purpose.

“acts contrary to our code of ethics”

“the facts point to a contrary conclusion”

A relation of direct opposition.

A logical relation such that two propositions are contraries if both cannot be true but both can be false.

Exact opposition.

“public opinion to the contrary he is not guilty”