the.com/contrapositive
logic's plot twist: flip it, negate it, and somehow it's still the same statement.
means In logic, the contrapositive of a conditional statement 'if P then Q' is 'if not-Q then not-P' — a flipped-and-negated version that is always logically equivalent to the original.
from Built from Latin pieces: contra, 'against,' plus ponere, 'to place' (its past participle positus gives us 'positive,' 'position,' and 'posit'). So a contrapositive is literally something 'placed against' — the statement set opposite to the original. The term comes from the vocabulary of formal logic, a cousin of the older 'contraposition' that medieval logicians used for exactly this kind of flip-and-negate maneuver.
- equal truth
- Always shares truth value with the original statement
- the flip
- If P then Q becomes if not-Q then not-P
- proof trick
- Mathematicians prove it when the direct route fails
- fake twins
- Converse and inverse only look equally valid
- ancient roots
- Aristotle's logic toolkit already wielded this move