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.  

 A: In Mathematics "if and only if" gives you information about both sides of the sentence. 
Using your example "I will go home if and only if it is not raining."
Assuming you did go home we conclude that it's not raining, and the other way around assuming it's not raining we conclude that indeed you did go home. 
On the other hand in English it's misunderstood and mostly used like a one way arrow.
More of a visual example is the arrow that is a symbol for if and only if 
$$\alpha \leftrightarrow \beta $$ 
which can also be written as 
$\alpha \rightarrow \beta$ and $\beta \rightarrow \alpha$
(when $\rightarrow$ represents if)
A: The ''if'' part tells you that "it's not raining" implies that "you will go home" and equivalently that "you don't go home" implies that "it's raining."
I think this is because we didn't usually use if and only if in our lives so just have more caught on the either part (??
A: 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 $False \leftrightarrow False = True$!
