## Question about a type of LG rule.

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montykarl91

Posts: 4
Joined: Sun Jul 14, 2013 9:47 pm

### Question about a type of LG rule.

Hey guys, I know this is a common theme in some questions, but it's just something that does not make much logical sense to me and I hoped someone could explain it so I can understand. Thanks a lot in advance.

One of the rules in PT 56, Logic Game 2 says: "Grace helps move the sofa if, but only if, Heather helps move the recliner." This seems to me to say that if Heather moves the recliner, then Grace will move the sofa. However, to obtain the full rule, 7sage says that it goes both ways. If Grace moves the sofa, Heather will always move the recliner. This just doesn't make sense to me. It seems like it's trying to say something like. You definitely used milk if you have ice cream. That makes sense. But then it apparently also means you definitely used ice cream if you have milk. I don't understand why it goes both ways. Can someone explain it so it makes sense to me?

ScottRiqui

Posts: 3637
Joined: Mon Nov 29, 2010 8:09 pm

### Re: Question about a type of LG rule.

montykarl91 wrote:Hey guys, I know this is a common theme in some questions, but it's just something that does not make much logical sense to me and I hoped someone could explain it so I can understand. Thanks a lot in advance.

One of the rules in PT 56, Logic Game 2 says: "Grace helps move the sofa if, but only if, Heather helps move the recliner." This seems to me to say that if Heather moves the recliner, then Grace will move the sofa. However, to obtain the full rule, 7sage says that it goes both ways. If Grace moves the sofa, Heather will always move the recliner. This just doesn't make sense to me. It seems like it's trying to say something like. You definitely used milk if you have ice cream. That makes sense. But then it apparently also means you definitely used ice cream if you have milk. I don't understand why it goes both ways. Can someone explain it so it makes sense to me?

It's the "but only if" part of the rule that makes it biconditional. When you see "A if, and only if, B", or "A if, but only if, B", then the rule looks like this:

B <--> A

See how the arrows go in both directions? That means that either A and B must both be true, or they must both be false.

In the game example you gave, it would be:

HR<-->GS

So either Heather moves the recliner AND Grace moves the sofa, or neither one happens.

Trajectory

Posts: 101
Joined: Sat Feb 09, 2013 5:04 pm

### Re: Question about a type of LG rule.

As far as I remember reading about how "if, and only if" turns into a bi-conditional (and what made most sense to me) is that its easier to grasp if its broken down between the comas.

A if, and only if, B.

So we have, A if B.
B--->A

Next, A only if B
A--->B

And we get:
A<--->B

objection_your_honor

Posts: 625
Joined: Sat Feb 11, 2012 2:19 pm

### Re: Question about a type of LG rule.

I think OP understands how to translate it formally, but just isn't sure why the grammatical sentence should be translated in that way.

"A if, and only if, B" is really making two statements:

If B, A. (B --> A)

If B occurs, A occurs.

A only if B. (A --> B)

If A occurs, B occurs.

Combined you have the bi-conditional.

Edit: Just realized this is what the above poster said.

bp shinners

Posts: 3086
Joined: Wed Mar 16, 2011 7:05 pm

### Re: Question about a type of LG rule.

Yep, the key here is, as Scott said, "if and only if". "If" introduces the sufficient; "only if" the necessary. With the and/but, it means that both terms are sufficient and necessary for each other. I either have both, or I have neither.

azditamo

Posts: 87
Joined: Mon Jun 03, 2013 10:45 pm

### Re: Question about a type of LG rule.

BP LG does a good job on this like the guy above me said. If is the sufficient condition and in a sentence like if it is rainng my car is wet rain is the sufficient condition and car wet is the necessary condition. Only if brings about a necessary condition and in the same sentence if it was structured to say my car is wet only if it was raining. Then rain is the necessary condition. In a if and only if they work off one another if it rainng then your cars is wet and only if your car is wet is it rainng. Both need to happen for the statement to occur of not then or falls apart. Also of imam wrong please correct me. Thank you

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