Propositions are contrary if they cannot both be true (though they both may be false). Propositions are contradictory when the truth of one implies the falsity of the other, and conversely.
Two properties are contraries if their intersection is null and their union is a whole. A merism is a rhetorical combination of two contrary terms that refers to an entirety. E.g., “young and old” refers to everyone.
The privation of a property is the contradictory opposite property, as disease is the privation of health (Aristotle Metaphysics Z 7.1032b3-5). St. Augustine argued that evil is the privation of good. There can be good without evil, but not evil without good.
A negation presupposes an affirmation but an affirmation doesn’t presuppose a negation. There must be something to negate for negation to have an effect. Contraries presuppose one another. E.g., there is no young without old, no up without down.
In symbolic logic, contradictories are represented by contrary symbols. The closest to representing contradictories is to represent the positive as unmarked and the privation as marked. This is what the Laws of Form does.