If and only if

From Fresh Dictionary

English

Phrase

if and only if

1. (Mathematics) The logical equivalence of two popositions A and B.If and only if is abriviated as iff or <math>\iff</math>. A if and only if B means:

   If A then B and if B then A

   A implies B and B implies A

2. (Logic) The binary operator <math>\iff</math>, true exactly when both inputs are either both true or both false. Logically equivalent to negation of XOR. In infix notation, it has values in the Boolean domain {0,1}:

   (0 <math>\iff</math> 0) = 1
   

   (0 <math>\iff</math> 1) = 0
   

   (1 <math>\iff</math> 0) = 0
   

   (1 <math>\iff</math> 1) = 1