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

Thanks

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 $(A \Rightarrow B) \land (B \Rightarrow A)$
