Bi-implication Relation

A Bi-implication Relation is a Boolean Logic Relation/Propositional Formula Connective where ...

• AKA: iif ↔, Bi-implication, Bi-implication Connective, Bi-implication Operation, Logical Bi-implication, Logical Bi-implication Relation, Biconditional Logical Connective, ≡, If and only if, ⇔.
• Context:
  • It has Truth Table:

    • A	B		A↔B
      T	T		T
      T	F		F
      F	T		F
      F	F		T

• See: Implication Relation.

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References

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/If_and_only_if
  • If and only if, in logic and fields that rely on it such as mathematics and philosophy, is a biconditional logical connective between statements. In that it is biconditional, the connective can be likened to the standard material conditional ("if") combined with its reverse ("only 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. The connective is thus an "if" that works both ways.
  • In writing, common alternative phrases to "if and only if" include iff, Q is necessary and sufficient for P, P is equivalent (or materially equivalent) to Q (compare material implication), P precisely if Q, P precisely (or exactly) when Q, P exactly in case Q, and P just in case Q. Many authors regard "iff" as unsuitable in formal writing; others use it freely.
  • In logic formulas, logical symbols are used instead of these phrases; see the discussion of notation.

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