## 'if AND only if' VS 'if BUT only if'

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Zeta

Posts: 70
Joined: Mon Nov 12, 2012 7:33 pm

### 'if AND only if' VS 'if BUT only if'

is there any difference in the diagramming of the two?

jump_man

Posts: 188
Joined: Sun Apr 04, 2010 12:05 am

### Re: 'if AND only if' VS 'if BUT only if'

Zeta wrote:is there any difference in the diagramming of the two?

Why don't you try it out and see if you get to the same answer (ideally, the correct answer)

Zeta

Posts: 70
Joined: Mon Nov 12, 2012 7:33 pm

### Re: 'if AND only if' VS 'if BUT only if'

A <--> B

TheMostDangerousLG

Posts: 1545
Joined: Thu Nov 22, 2012 4:25 am

### Re: 'if AND only if' VS 'if BUT only if'

Zeta wrote:I get the same answer.

A <--> B

Maybe it would be useful if you try thinking of "if and only if" in terms of two distinct statements. So for example, "A if and only if B" can be seen as "A if B" AND "A only if B" (which is functionally equivalent to "but only if"). If you try diagramming them, you should see the difference in the relationship:

"A if and only if B" = "A if B" and "A only if B":
1. "A if B" (which is of course equivalent to "if B, then A"): B --> A
2. "A only if B": ~ B --> ~ A

And then the contrapositive of the second statement being A --> B, you can see how it combines with the first statement to form the statement you posted, A <--> B.

The difference between that and "A but only if B" is that B does not necessarily "trigger" A. You know that if you have A, you must also have B ("but only if"), but you don't necessarily know the opposite to be true. So it would just be written as: A --> B. And from there the contrapositive, ~ B --> ~ A (if not B, then you can't have A). But knowing that you have B does not imply that you have A (as in the first statement above / "A if B").

TL;DR: "A if and only if B" = A <--> B, "A but only if B" = "A --> B".

Gah, that was terribly long-winded, sorry! Middle of an all-nighter = tired rambling.

KaplanLSATInstructor

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

### Re: 'if AND only if' VS 'if BUT only if'

OP,

I just want to clarify, since I believe the above poster missed a key word in your original question. (The above poster was discussing X, but only if Y -- leaving out the crucial "if" immediately before the "but.")

If you're told "X if, and only if, Y"... this is EXACTLY the same as being told "X if, but only if, Y."

In both cases, Y is both sufficient to guarantee X (because of the "if") and necessary for X (because of the "only if"). So you get two pieces of Formal Logic for the price of one:

X --> Y
Y --> X

And, of course, both contrapositives are also valid. Some people like to use the double arrow notation (X <--> Y), but that's a personal decision.

Hope this helps.

- Chris

BeenDidThat

Posts: 695
Joined: Thu Feb 03, 2011 12:18 am

### Re: 'if AND only if' VS 'if BUT only if'

KaplanLSATInstructor wrote:OP,

I just want to clarify, since I believe the above poster missed a key word in your original question. (The above poster was discussing X, but only if Y -- leaving out the crucial "if" immediately before the "but.")

If you're told "X if, and only if, Y"... this is EXACTLY the same as being told "X if, but only if, Y."

In both cases, Y is both sufficient to guarantee X (because of the "if") and necessary for X (because of the "only if"). So you get two pieces of Formal Logic for the price of one:

X --> Y
Y --> X

And, of course, both contrapositives are also valid. Some people like to use the double arrow notation (X <--> Y), but that's a personal decision.

Hope this helps.

- Chris

^^^ what he said (want to clarify because the poster two above missed it)

"And" and "But" have the same logical content, but the word "but" serves as a prelude to the second clause of a sentence, indicating that it will qualify the first clause.

It would be very strange to use say "a gun will shoot if but only if it has a bullet in it." It should be "a gun will shoot if and only if it has a bullet in it."

Using "but" here makes little sense because there's no definitive content preceding the "but" that would need qualification, thanks to the first "if."

scottyc66

Posts: 717
Joined: Mon Oct 22, 2012 4:19 pm

### Re: 'if AND only if' VS 'if BUT only if'

Zeta wrote:is there any difference in the diagramming of the two?

Tons of responses and text to a very simple question, they're the same

blackandstrong

Posts: 110
Joined: Sat Nov 17, 2012 12:10 pm

### Re: 'if AND only if' VS 'if BUT only if'

scottyc66 wrote:
Zeta wrote:is there any difference in the diagramming of the two?

Tons of responses and text to a very simple question, they're the same

LOL. I was going to say that. No difference between the two.

TheMostDangerousLG

Posts: 1545
Joined: Thu Nov 22, 2012 4:25 am

### Re: 'if AND only if' VS 'if BUT only if'

BeenDidThat wrote:
KaplanLSATInstructor wrote:OP,

I just want to clarify, since I believe the above poster missed a key word in your original question. (The above poster was discussing X, but only if Y -- leaving out the crucial "if" immediately before the "but.")

If you're told "X if, and only if, Y"... this is EXACTLY the same as being told "X if, but only if, Y."

In both cases, Y is both sufficient to guarantee X (because of the "if") and necessary for X (because of the "only if"). So you get two pieces of Formal Logic for the price of one:

X --> Y
Y --> X

And, of course, both contrapositives are also valid. Some people like to use the double arrow notation (X <--> Y), but that's a personal decision.

Hope this helps.

- Chris

^^^ what he said (want to clarify because the poster two above missed it)

"And" and "But" have the same logical content, but the word "but" serves as a prelude to the second clause of a sentence, indicating that it will qualify the first clause.

It would be very strange to use say "a gun will shoot if but only if it has a bullet in it." It should be "a gun will shoot if and only if it has a bullet in it."

Using "but" here makes little sense because there's no definitive content preceding the "but" that would need qualification, thanks to the first "if."

Oh geez, you're right! Feel like an idiot; sorry for the useless post. (Shall hereby refrain from posting in the middle of the night without sufficient caffeine.)

Zeta

Posts: 70
Joined: Mon Nov 12, 2012 7:33 pm

### Re: 'if AND only if' VS 'if BUT only if'

i appreciate the explanations a lot. they help a lot more than just, 'they're the same.'