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 “ if and if .” Slightly more formal, one would say “ implies and implies .” 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.
|Date of creation||2013-03-22 11:53:06|
|Last modified on||2013-03-22 11:53:06|
|Last modified by||Mathprof (13753)|