biconditional (original) (raw)

1 Biconditional

Symbolically, the biconditional is written as

The biconditional function is often written as “iff,” meaning “if and only if.”

This fact is important to recognize when writing a mathematical proof, as both conditionals must be proven independently.

2 Colloquial Usage

The only unambiguous way of stating a biconditional in plain English is of the form “b if a and a if b.” Slightly more formal, one would say “b implies a and a implies b.” The plain English “if” may sometimes be used as a biconditional. One must weigh context heavily.

For example, “I’ll buy you an ice cream if you pass the exam” is meant as a biconditional, since the speaker doesn’t intend a valid outcome to be buying the ice cream whether or not you pass the exam (as in a conditional). However, “it is cloudy if it is raining” is not meant as a biconditional, since it can obviously be cloudy while not raining.