All that is necesary for vs if, and only if

[RuonanW40]

what is the difference between "if and only if" and "All that is necessary for“？

[ohthatpatrick]

"if and only if" is two different conditional triggers.

if = sufficient condition (left side)
only if = necessary condition (right side)

"if and only if"
"then and only then"
"when and only when"

These all give us two different conditional ideas.

If I say "if and only if Peter is 3rd", then there is a rule in which Peter is 3rd is sufficient

P is 3 --> _____

and a rule in which Peter is 3rd is necessary

____ --> P is 3


If I complete that sentence, with something like "Mary is 1st if and only if Peter is 3rd", we would get

P is 3 --> M is 1
and
M is 1 --> P is 3

Instead of writing both rules, we tend to represent these "biconditional" statements with double sided arrows, to indicate that the logic flows in both directions.
P is 3 <---> M is 1

Or, you can represent them as either/or's. Either both things happen or both things don't.

P is 3 and M is 1 ..... or ..... P is not 3 and M is not 1


"All that is necessary for" is an incredibly rare conditional trigger. I think I've only seen it once on LSAT ever.

Since I didn't have a pre-established playbook for it, I just tried to think of a true sentence that would use "all that is necessary".

Shooting yourself in the brain is all that is necessary to kill you.
Telling your mom you love her is all that is necessary to make her smile.

It feels like "all that is necessary" is just a sufficient condition (ironically, since it's using the word 'necessary').

I would diagram those rules as
Shoot yourself in brain --> kill yourself
Tell mom you love her --> mom smiles

They aren't saying that shooting yourself is the ONLY way to kill you, or that saying "I love you" is the ONLY way to make Mom smile ... they're just saying "it would be enough / it's all you need to do "

I think in other contexts we might hear it as necessary and sufficient.
"All you need to get into this movie is $5"

That sounds like
if you pay $5, you'll get in (suff)
if you don't pay $5, you won't get in (nec)

I feel more comfortable that "all that is necessary" would be sufficient in every context. It might be too loose or colloquial an expression to guarantee necessity, as the shooting yourself / loving mom examples attempted to show.

Overall, make sure you have a plan for biconditionals, but worry very little that you'll see "all that is necessary" again for another 20 tests.