What is the difference between only if and iff?

I have read this question. I am now stuck with the difference between “if and only if” and “only if“. Please help me out.



Let’s assume A and B are two statements. Then to say “A only if B” means that A can only ever be true when B is true. That is, B is necessary for A to be true. To say “A if and only if B” means that A is true if B is true, and B is true if A is true. That is, A is necessary and sufficient for B. Succinctly,

A \text{ only if } B is the logic statement A \Rightarrow B.

A \text{ iff } B is the statement (A \Rightarrow B) \land (B \Rightarrow A)

Source : Link , Question Author : Community , Answer Author : michael

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