In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false.
The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, P if and only if Q means that P is true whenever Q is true, and the only case in which P is true is if Q is also true, whereas in the case of P if Q, there could be other scenarios where P is true and Q is false.
In writing, phrases commonly used as alternatives to P "if and only if" Q include: Q is necessary and sufficient for P, for P it is necessary and sufficient that Q, P is equivalent (or materially equivalent) to Q (compare with material implication), P precisely if Q, P precisely (or exactly) when Q, P exactly in case Q, and P just in case Q. Some authors regard "iff" as unsuitable in formal writing; others consider it a "borderline case" and tolerate its use.In logical formulae, logical symbols, such as

{\displaystyle \leftrightarrow }

{\displaystyle \Leftrightarrow }
, are used instead of these phrases; see § Notation below.

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Did you know?

Credit is the trust which allows one party to provide money or resources to another party wherein the second party does not reimburse the first party immediately, but promises either to repay or return those resources at a later date.

Lenders want to make sure all their bases are covered before they extend you credit. That means they may look at factors other than your credit score to determine whether to lend you money. Your employment status also can play a role: If your income is too low or you haven’t been at your current workplace long, those factors could weigh against you.

Errors can come in a variety of forms. You may not have been credited for a payment you made, or you may have been charged for a purchase you didn’t make. A debt might be listed more than once, or your balance might be wrong.