if, but only if

[Tobias Beecher]

hey guys here's a rule that i struggled during the december test.....can someone please clearify it a little bit?

game 3, Q 18-22:

Nation X exports Soybean if, but only if, Nation Y does also.

so if X exports soybean, then Y must also export soybean.

But when Y exports soybean...does X have to export soybean?

in the PS LRB it says that it's a "vice versa" relationship if you see "if and only if" and the like but I don't really get it.

Thanks!

[cascagrossa]

i interpreted it as just being "only if" and didnt miss any questions, but people here with a background in formal logic say that it is infact a biconditional just like "if and only if."

[mcleod13]

Can someone elaborate more on this, I don't quite understand it

[BigTex]

Logically, but = and. In terms of logic, there is no difference between the two. People just use "but" when the two facts being conjoined are seemingly at odds with one another. For example:

"I got into Harvard, but i got a 155 on the LSAT"
is logically equivalent to
"I got into Harvard, and i got a 155 on the LSAT"

"A if, but only if B" is logically the same as "A if, and only if B". A implies B and B implies A.

[TheZooker]

Right.  I interpreted this as if and only if on the Dec test and didn't miss any.  The fact that Casca also didn't miss any is not surprising, since he just took a more conservative slant to the rule by only using the only if part.  It might have made it a little more time consuming that way, but you wouldn't rule out any choices unnecessarily.

McLeod - There was a lot of discussion about this on a thread in teh Studying for the LSAT section after the test.  You might find it helpful.  The gist is that:

A only if B means        A -> B
and
A if B means             B -> A

These two combine to give A <--> B, that is, they always go together.