## "if and only if" clarification please!!

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bks6064

Posts: 4
Joined: Tue Jun 30, 2009 9:34 pm

### "if and only if" clarification please!!

My tutor has me all backwards on this now. I intitially prepped with Powerscore, but my Princeton Review tutor told me conflicting information.

Ok this is how I interpret it:

A if and only if B equates to a biconditional statement (right?)

A --> B & B --> A where either A/B is sufficient and necessary which is A <---> B. Either both are in or neither. Is this correct???

My tutor advised that it only means A ---> B, where B is only necessary and there is not a biconditional statement.

Also, is this interpreted any differently in LR vs Games?? Please chime in, thanks!

loveistheway

Posts: 28
Joined: Tue Oct 06, 2009 2:15 pm

### Re: "if and only if" clarification please!!

fire your tutor

umichgrad

Posts: 381
Joined: Wed Aug 26, 2009 11:53 am

### Re: "if and only if" clarification please!!

It is warm if and only if it is summer.

It is summer. Does it have to be warm? No. But if it is warm, it has to be summer.

straxen

Posts: 135
Joined: Thu Nov 19, 2009 3:39 am

### Re: "if and only if" clarification please!!

umichgrad wrote:It is warm if and only if it is summer.

It is summer. Does it have to be warm? No. But if it is warm, it has to be summer.

Wrong.

It does have to be warm. This has two parts.

It is warm if it is summer. = If Summer --> Warm
It is warm only if it is summer = If Warm --> Summer

loveistheway wrote:fire your tutor

+1

KaplanLSATInstructor

Posts: 53
Joined: Fri Sep 12, 2008 5:53 pm

### Re: "if and only if" clarification please!!

OP -- Your initial reaction was correct. "If and Only If" is a biconditional statement.

"X if and only if Y" means two things: X, if Y. and X only if Y.

The first translates to: Y --> X
The second translates to X --> Y

So, the basic idea is that if you have one, you must have the other. If you don't have one, you can't have the other.

It means the same thing in both LG and LR. For a perfect game to test this rule out, check out Game 4 of PrepTest 45.

theanswer

Posts: 27
Joined: Fri Sep 18, 2009 2:49 pm

### Re: "if and only if" clarification please!!

umichgrad wrote:It is warm if and only if it is summer.

It is summer. Does it have to be warm? No. But if it is warm, it has to be summer.

wrong.

A (warmth) if and only if B (summer) breaks down into two clauses:

1. A occurs if B occurs. "It is warm if it is summer."

mapped the same as if B, then A. "If it is summer, then it is warm."

aka B------>A

2. A occurs only if B occurs. "It is warm only if it is summer."

A-->B

in sum A<--->B

dynomite

Posts: 143
Joined: Sat Jan 30, 2010 6:58 pm

### Re: "if and only if" clarification please!!

The key here is that this statement is structured in a subtly (but crucially) different way.

You're used to seeing statements as: "If A, then B." (A-->B)

But the statement "A if B" is the OPPOSITE of what you normally see, and translates as "If B, then A." (B-->A)

As said above, "if and only if" translates into a simple entity block: [AB]

bks6064

Posts: 4
Joined: Tue Jun 30, 2009 9:34 pm

### Re: "if and only if" clarification please!!

Thanks everyone!

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