Hi Marce,
Thanks for the question! The double arrow can be tough to learn at first, so I'll post a quick answer here to get you started, and then come back in an hour or two and expand on it a bit more. If you have further questions in the meantime after reading this, just post them below and I'll answer those too
The key is the placement of the conditional indicators ("if" & "only if") in the sentence. "If" is a sufficient condition indicator, so whatever it modifies will be the sufficient condition; "only if" is a necessary condition indicator so whatever it modifies will be the necessary condition. Knowing that is the first step to breaking this down systematically.
Now, to make things further confusing, "if and only if" is two statements combined into one sentence. It looks like this when separated out:
A
if B
and
A
only if B
Ok, with those two parts isolated, we can diagram each portion. Let's start with: "A
if B"
- "If" modifies B, so B is the sufficient condition. The remainder, A, is the necessary condition, leading to the following diagram:
B 
A
It "looks" backwards, but according to the logic it's correct. Tricky, right?
The second portion is: "A
only if B"
- "Only if" modifies B, and "only if" introduces a necessary condition, so B is the necessary condition. The remainder, A, is then the sufficient condition, leading to the following diagram:
A B
Returning to our first view of the sentence, all of the above info combined appears as:
A
if B:
B
A
and
A
only if B:
A
B
When we add those two arrow diagrams together, the result is our friendly double-arrow:
A
B
That's a start, and please let me know if that helps. I'll add a few more links and additional info to this in just a bit, to help lock in the idea
Thanks!
