Only and Only ifs

[Kristinav10]

I'm going over the Conditional Logic Quiz and I'm very confused on "only" "only if" and "if and only if". I'm confused as to when to place the "only" at the sufficient or the necessary side of the statement and contrapositive. Is there a specific rule to differentiate when to place the "only's" at the beginning or end of a statement when diagramming. I need help!!

[ohthatpatrick]

Yup, it's dumb but there are rules you can memorize.

If = left side
Only If = right side

That's always.

So
If X happens, Y happens
X --> Y

Only if X happens, Y happnes
Y --> X

X happens if and only if Y happens

Because it said "if Y happens", we know
Y ---> X
and because it said "only if Y happens", we know
X ---> Y

Since Y leads to X, and X leads to Y, we call this a BI-conditional.
It goes both ways, so we can write it ONCE, by using a double sided arrow.
X <----> Y

Bi-conditionals are very rare on LSAT, and they should stick out to your ears, because they're the only conditional triggers that have two part rhythm. They have two-part rhythms because they are telling us that a certain idea is both a LEFT side idea and a RIGHT side idea:
if and only if
if but only if
then and only then
when and only when

If = Left side
When = Left side

Only if = right side
Only when = right side

That's always.

Now, the messier situation is "only" vs. "the only".
Only = right side
The only = left side

Only X's are Y
Y --> X

The only things that are X are Y
X --> Y

"The only" is very rare.
90% of the time you see the word 'only' on LSAT, it's showing up as 'only' or 'only if', both of which are right side ideas.

So a safe (but not always accurate) rule of thumb is:
draw an arrow through ONLY
That will tell your eyes that the idea after the word ONLY is a right side idea; it belongs on the right side of the arrow.

"The only" exception is "The only".
"The only" is "the only" time that 'only' goes on the left.

[BasundharaM943]

My question has to do with the Drill on page 69 of the LR book...in re: If to Only If.

The question asks the following:

3) Only if the car is new is it in good shape
a- The car is in good shape if, and only if, it is new.
b- The car is new if, and only if, it is in good shape
c- If the car is in good shape, then it is new
d- If the car is new, then it is in good shape. [/list]

We know C is true because the conditional would read GS —> N. But why would A also not be true? The car is in good shape only if it is new, according to the question, which would make answer choice A valid as well, right?

[A B]

Hi ! To answer your question about the drill on page 69 of the LR book, I think the reason A is incorrect is because it's setting up a biconditional statement, and a biconditional is the sufficient and the necessary, so, if we wrote out A, it would look like:

if New --> Good shape
if good shape --> new

But that's not actually true for us. Our original statement is only: Good shape --> new
So, including that extra statement that comes along with the bi-conditional makes A incorrect.

Let me know if I can clarify anything (and also if you think I'm wrong!, but I think this should be correct!)