If and only if, which direction is which? I can never figure out (because the English language is imprecise) which part of "if and only if" means which implication.
($A$ if and only if $B$) = $(A \iff B)$, but is the following correct:
($A$ only if $B$) = $(A \implies B)$
($A$ if $B$) = $(A \impliedby B)$
The trouble is, one never comes into contact with "$A$ if $B$" or "$A$ only if $B$" using those constructions in everyday common speech.

It's easier to work out if you have a specific example:
Let 
A:I am a parent
B:I have a child
I am a parent if and only if I have a child has two parts:
I am a parent if I have a child
   can be rephrased:
   If I have a child, then I am a parent. B => A
I am a parent only if I have a child
   can be understood to mean:
   if I do not have a child, then I am not a parent: ~B -> ~A
But this is logically equivalent to
   if I am a parent, then I have a child: A=> B
So the "if and only if" locution implicitly involves some grammatical transformations. The meaning may not be immediately obvious, but it can be worked out. 
