Topic: If And Only If


Summary

The phrase "if and only if", which is often shortened to "iff", is a Logical term often found when discussing Mathematics and Philosophy.

An equivalent expression of iff is: Necessary and Sufficient. And is sometimes called: Equivalence.

Definition
p q p iff q
T T T
T F F
F T F
F F T
Exclusive Nor

Iff is the same thing as the: exclusive nor.

Or, in other words, is the same thing as: not (p xor q).

Symbols

The symbol I've seen used most for representing iff, is a horizontal double shafted, double pointed arrow. So there's 2 shafts/lines (like on an Equal Sign), and each end of it has an Arrow Head.

I've also read that 3 horizontal lines is sometimes used to represent iff. I.e.,....

As in....


  p  q
    

For those involved in Web Development, this symbol can be generated in HTML with the code....

≡

In many programming languages, iff is written as....

==

As in....


  if (a == 5) {
      x := y * 2;
  }
    
-- Mirza Charles Iliya Krempeaux
       

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