## Relative Statements

Prepare for the LSAT or discuss it with others in this forum.
CREATION

Posts: 31
Joined: Mon Mar 19, 2012 8:46 pm

### Relative Statements

If I say that as A increases, B increases.

And I know that B has increased and A exists.

I cannot infer that A has increased, correct?

I believe I can infer that A decreasing will lead to B decreasing. But then again, why couldn't A decrease while B still increases?

Does anyone have a grasp on these relative statements?
Last edited by CREATION on Mon Apr 16, 2012 11:48 pm, edited 1 time in total.

Clearly

Posts: 4191
Joined: Sat Feb 11, 2012 4:09 pm

### Re: Issue of Relative Statements

CREATION wrote:If I say that as A increases, B increases.

And I know that B has increased and A exists.

I cannot infer that A has increased, correct?

I believe I can infer that A decreasing will lead to B decreasing. But then again, why couldn't A decrease while B still increases?

Does anyone have a grasp on these relative statements?

I don't believe your inference that a decreasing will lead to b decreasing to be valid

LSAT Blog

Posts: 1257
Joined: Mon Dec 07, 2009 9:24 pm

### Re: Issue of Relative Statements

Clearlynotstefan wrote:
CREATION wrote:If I say that as A increases, B increases.

And I know that B has increased and A exists.

I cannot infer that A has increased, correct?

I believe I can infer that A decreasing will lead to B decreasing. But then again, why couldn't A decrease while B still increases?

Does anyone have a grasp on these relative statements?

I don't believe your inference that a decreasing will lead to b decreasing to be valid

(I'm going to use "up" and "not up" to make things even simpler than "increase" and "decrease.")

A up -> B up

Therefore, "B not up, A not up"

That's all you can infer.

You cannot infer "B up -> A up"

Nor can you infer "A not up -> B not up"

"A not up" doesn't tell you anything about what B's doing.

"A up" is the only info that tells you what B's doing.

CREATION

Posts: 31
Joined: Mon Mar 19, 2012 8:46 pm

### Re: Issue of Relative Statements

The lower my blood pressure, the lower my risk of a heart attack.

It would seem that the higher my blood pressure, the higher my risk of heart attack. That seems to be valid? Why isnt my first example

dkb17xzx

Posts: 403
Joined: Wed Jan 20, 2010 6:25 pm

### Re: Relative Statements

I think you are confusing correlations and conditional statements.

CREATION

Posts: 31
Joined: Mon Mar 19, 2012 8:46 pm

### Re: Relative Statements

So do you or do you not agree with the idea that the prior post of blood pressure is valid

Clearly

Posts: 4191
Joined: Sat Feb 11, 2012 4:09 pm

### Re: Relative Statements

CREATION wrote:So do you or do you not agree with the idea that the prior post of blood pressure is valid

Logically, it's invalid as far as the LSAT goes. Correlation is one thing, a valid principle. But conditional logic (lsat wise) doesn't account for this. For example, write a paradox question with that same stimulus.

Blood pressure goes up then heart attack goes up, but blood pressure going low, doesn't reduce the chance of heart attack
Which of the following resolves the apparent paradox:

As blood pressure falls too low, the heart works harder to move blood, and initiates a heart attack
As blood pressure falls, veins constrict causing heart attack
etc.

If you could see this principle in this form, you might see what I'm saying.

As far as conditional logic goes, you can't chart anything but the contrapositive of one rule. If the rule or a contrapositive of a rule should tie in with another rule, then you might be able to expand on the concept...but with what you gave, the only thing to be said is

A up -> B up
~B up -> ~A up

CREATION

Posts: 31
Joined: Mon Mar 19, 2012 8:46 pm

### Re: Relative Statements

Are you really saying that:

The lower my blood pressure, the lower my risk of a heart attack.

...Would not allow us to infer that the higher my blood pressure, the higher my risk?

That just seems to be a valid inference.

shifty_eyed

Posts: 1925
Joined: Fri Oct 02, 2009 8:09 pm

### Re: Relative Statements

CREATION wrote:Are you really saying that:

The lower my blood pressure, the lower my risk of a heart attack.

...Would not allow us to infer that the higher my blood pressure, the higher my risk?

That just seems to be a valid inference.

No. It may seem like a common sense fact, but it doesn't logically follow simply from that statement alone.

ben4847

Posts: 788
Joined: Mon Nov 07, 2011 11:38 pm

### Re: Relative Statements

As this thread gets longer with incorrect responses, I find it more amusing.

This does not mean that if I found it more amusing, it would be longer.

flem

Posts: 12882
Joined: Mon Oct 10, 2011 6:44 pm

### Re: Relative Statements

shifty_eyed wrote:
CREATION wrote:Are you really saying that:

The lower my blood pressure, the lower my risk of a heart attack.

...Would not allow us to infer that the higher my blood pressure, the higher my risk?

That just seems to be a valid inference.

No. It may seem like a common sense fact, but it doesn't logically follow simply from that statement alone.

Yup

Correct

One thing could happen without the other. Couldn't you have a heart attack without having low blood pressure?

If your blood pressure is low, your risk of high attack is low.

BP ----> LR

The correct contrapositive would be:

~LR ---> ~BP

If your risk of heart attack is not low, your blood pressure is not low.

Incorrect

To assume what you're saying would be:

~BP ---> ~LR

Which, in LSAT terms, is a mistaken negation. You're forgetting to flip the necessary and sufficient conditions.

I realize this makes no sense from a common sense standpoint, but it's purely logic.

CREATION

Posts: 31
Joined: Mon Mar 19, 2012 8:46 pm

### Re: Relative Statements

You guys are so caught up on contrapositives when it is not at issue here. It seems to be a math thing.

But the example of the lower the BP, the lower the risk of heart attack.....

Can't I say that the higher the BP, the higher the risk of heart attack?

X3 Y3

X2 Y2

X1 Y1

It seems that the BP going down the X column would also show that from where it came from (higher) implies a higher Y point.

Example: If X3 goes down to X1, we know that Y goes from Y3 to Y1, yet I can see that from where I came from (X3) that this is a higher point of blood pressure, and its risk of heart attack is higher at Y3.

flem

Posts: 12882
Joined: Mon Oct 10, 2011 6:44 pm

### Re: Relative Statements

CREATION wrote:You guys are so caught up on contrapositives when it is not at issue here. It seems to be a math thing.

But the example of the lower the BP, the lower the risk of heart attack.....

Can't I say that the higher the BP, the higher the risk of heart attack?

X3 Y3

X2 Y2

X1 Y1

It seems that the BP going down the X column would also show that from where it came from (higher) implies a higher Y point.

Example: If X3 goes down to X1, we know that Y goes from Y3 to Y1, yet I can see that from where I came from (X3) that this is a higher point of blood pressure, and its risk of heart attack is higher at Y3.

In the LSAT realm, ignore all common sense and outside knowledge. In this scenario, you simply don't know enough info to make that inference.

suspicious android

Posts: 919
Joined: Tue Feb 09, 2010 4:54 pm

### Re: Relative Statements

In your original example, the language was not enough to show a correlation between A and B, so it was possible, as LSAT blog noted, that A and B move independently.

In your second example, if you really know that lower blood pressure means lower risk of heart attack, then that is enough to establish a correlation. As such, higher blood pressure would mean higher risk of heart attack.

It comes down to the language used to connect the two ideas. "If low A, then low B" doesn't guarantee a correlation, because it only provides half of the needed relationship. "LowER A then lowER B" tells us that for any particular value of A, there is a corresponding B value that could be at least partially determined by finding A. So if the correlation were perfect, knowing Bs value would give you As value.

CREATION

Posts: 31
Joined: Mon Mar 19, 2012 8:46 pm

### Re: Relative Statements

The lower bp is, the lower the risk of HA

Is that a perfect correlation?

I thought my first example is the same idea as the one above.

As bp goes down, risk of HA goes down.

Is that not the same thing?

I see that you are saying lowER and lowER give us justification for inferring higher and higher but why not more and more.....less and less.

Both of these examples are correlations and I'm not sure what a perfect correlation is.