Biconditional
A conditional and the converse of this need to be true, in which case "if only if " is used with the hypothesis and the conclusion of the conditional to make the biconditional.

Conditional
Refers to an "if p then q" statement.

Contrapositive
In a conditional statement "if p then q", the contrapositive is "if not p then not q", and always have the same truth value as the original conditional.

Converse
In a conditional statement "if p then q", the converse is "if q then p".

Counterexample
A particular instance that makes one statement false.

Inverse
A form of conditional; "if not p, then not q".