If and Only If

AKA iff

Definitions

If and Only If

Definition

Iff (), when both A and B have the same truth value
T T T
T F F
F T F
F F T
Remark

and

(see universally quantified statement, implication)

Proofs

Tip

Proving
To prove iff, we need to prove in both directions

Proof Method - IFF

Proof

  1. To prove the statement , it is equivalent to prove both the implication and its converse
  2. To prove the universally quantified statement , do one of the following
    1. Let be an arbitrary element of , and prove both the implication and its converse
    2. Prove both the universally quantified implication and its universally quantified converse