the.com/biconditional
the logic gate that demands both directions agree before it grants you the truth
means In logic, a statement of the form 'P if and only if Q,' which is true exactly when both parts share the same truth value—both true or both false.
from A modern, transparent compound: the Latin prefix 'bi-' ('two') bolted onto 'conditional,' itself from Latin 'conditio' (a stipulation or agreement, from 'condicere,' 'to agree together'). The 'conditional' is logic's old 'if-then'; doubling it with 'bi-' captures the two directions an 'if and only if' insists upon—a coinage born of formal logic and mathematics, where the phrase 'if and only if' (sometimes squeezed to 'iff') reigns.
- symbol
- Written as a double-headed arrow, pointing both ways
- plain words
- Means if and only if, both sides locked together
- truth trick
- True only when both parts share the same value
- math shorthand
- Often abbreviated iff in proofs and textbooks
- hidden inside
- Equals two conditionals joined, each direction proved separately