Is meaning of same thing is different in mathematical logic and english? Is meaning of "if and only if" is different in mathematical aspects and English aspect?
let's take an example:  

Example:I will go home if and only if it is not raining.
  Now according to me in english aspect ,I cannot comment anything about rain if i did not go home,
  but in mathematical aspect, I am sure that it is raining if i didn't go home,because in mathematics if and only if represent equivalence logic.  


There is indeed a mismatch between the way we typically treat the 'if and only if' statement in English (or any other natural language) and the way we treat the logical $\leftrightarrow$. Take the following example:
'Mary lives in France if and only if Mary lives in Germany'
In any natural language would immediately say that this statement is false.
But if we suppose that Mary lives in Nigeria, then following the logical biconditional, we would evaluate it to $False \leftrightarrow False = True$!
