How do you say "if and only if" in Japanese?


I would like to know how to express mandatory conditions in Japanese. Since
Japanese distinguishes between different types of languages, I should probably
ask more precisely:

What is the right way to express equivalence statements (the kind a
mathematician might make) such as "The equation is satisfied if and only if
a>b"?

How do you express that you're going to do or that something will happen, only
if some condition is satisfied? ("I'll only go if you buy me an ice.", "The
plant will only grow if it is watered regularly.")




Two common ways of translating "if and only if" use the terms 必要十分条件
("necessary and sufficient condition") and 同値 ("equivalence").

> a > b は式 (15) である為の必要十分条件である。  
>  Equation (15) holds if and only if a > b.
>
> 式 （15） と「a>b」とは同値である。  
>  Equation (15) is equivalent to a > b.




Two common ways of translating "if and only if" use the terms 必要十分条件
("necessary and sufficient condition") and 同値 ("equivalence").

> a > b は式 (15) である為の必要十分条件である。  
>  Equation (15) holds if and only if a > b.
>
> 式 （15） と「a>b」とは同値である。  
>  Equation (15) is equivalent to a > b.

