Q16 - Therapist: The ability to trust

[ManhattanPrepLSAT1]

This is where the skilled use of conditional logic can really benefit someone.

Here's how I see it. I know that I rely heavily on conditional logic, whereas some others do not. If the notation I use is complete mumbo jumbo, let me know, and I'd be happy to take a different approach. There's more than one way to skin a cat!

~T --> ~MEC
~MEC --> I
==========
H --> T

(Formal Notation Key: T = Trust, MEC = Meaningful Emotional Connection, I = Isolated, H = Happy)

Let me reorganize it by taking the contopositive of both premises and putting the second premise first...

~I --> MEC
MEC --> T
=========
H --> T

Now the gap in the reasoning should be more clear.

H --> ~I

put into English reads, "If one is happy, then one does not feel isolated." - best expressed in answer choice (A)

I know this is a lot of steps and it may feel like this would take you too long on the test, but if you can master conditional logic, this question would never take you more than a minute.

(A) is the contrapositive of the gap that was stated above. One can put this into notation by using the key word "no." "No" introduces the sufficient condition, while implying the negation of the necessary condition. So answer choice (A) could be phrased, " If one is feeling isolated then that person does not feel happy."
and now into notation...

I --> ~H (note: this is the contrapositive of the gap above)

(B) does not help draw the conclusion. This would read

MEC --> H

combine it with

~I --> MEC

and we could infer

~I --> H (but we could not infer the conclusion)

(C) would read ~I --> T and would not help draw a conclusion about whether one can be happy.
(D) would read ~I some H. Remember in addition to conditional statements there also exist quantified statements "SOME" and "MOST" which this argument does not contain.
(E) would read T --> MEC and would not help draw a conclusion about whether one could be happy.


#officialexplanation

[ecmoloney]

These types of questions are the toughest for me (the ones with no ones, someones, anyones in particular). Anyone want to walk through this one?

[shaynfernandez]

This is what I came up with and I can't figure out why it is flawed.
The ability to trust other people is ESSENTIAL to happiness
H--->T
for WITHOUT trust there can be no meaningful emotional connections to another human being.
~EC--->~T
because WITHOUT is a necessary condition indicator. I don't understand how trust, which follows after "without" is a sufficient condition?
WITHOUT meaningful emotional connections to others we feel isolated.
Iso--->~EC

Any help on this problem would be greatly appreciated.

[ilona11223344]

This is what I came up with and I can't figure out why it is flawed.
The ability to trust other people is ESSENTIAL to happiness
H--->T
for WITHOUT trust there can be no meaningful emotional connections to another human being.
~EC--->~T
because WITHOUT is a necessary condition indicator. I don't understand how trust, which follows after "without" is a sufficient condition?
WITHOUT meaningful emotional connections to others we feel isolated.
Iso--->~EC

Any help on this problem would be greatly appreciated.

I think you might have mistaken the conditionals:

It should go like this-

"The ability to trust other people is essential to happiness"
-this is the conclusion & "is essential to" means that happiness is the sufficient condition or you could say that happiness guarantees trust

H-->T

-The rest of the stimulus is evidence and can be formulated like this:

EC --> T

EC - emotional connection
-whatever comes after WITHOUT is always the necessary condition and you negate the sufficient condition - in this case Emotional Connection

~I -> EC
I=Isolated
-again the use of WITHOUT

- you can combine the 2 premises & you get

~I-->EC-->T

Remember, the conclusion is : H-->T

so we're looking for something that says H-->~I

And (A) is the contrapositive of the above. Hope this helps!

[ManhattanPrepLSAT1]

Nice work ilona11223344! That's exactly right.

for WITHOUT trust there can be no meaningful emotional connections to another human being.
~EC--->~T
because WITHOUT is a necessary condition indicator. I don't understand how trust, which follows after "without" is a sufficient condition?

You have it correctly that trust is a necessary condition, but you also need to keep in mind that for every conditional relationship, there is also the contrapositive.

So if we can set up the statement WITHOUT trust there can be no meaningful emotional connections to another human being as:

EC ---> T

we can rephrase this as:

~T ---> ~EC

Nice discussion guys!

[shaynfernandez]

EC --> T

EC - emotional connection
-whatever comes after WITHOUT is always the necessary condition and you negate the sufficient condition - in this case Emotional Connection

This is what I don't under stand... the word that comes after without is "trust" so that makes it the necessary condition and the sufficient condition would be "meaningful emotional connection"

so wouldn't that result in

~EC --> ~T
or the contrapositive
T--> EC

Would appreciate the help extremely lost on these questions.

[ManhattanPrepLSAT1]

so wouldn't that result in

~EC --> ~T
or the contrapositive
T--> EC

But didn't you just say that the "trust" is the necessary condition? Your statement makes "trust" the sufficient condition.

If "trust" is the necessary condition, it should be

EC ---> T

Right?

[Favbe]

I am having trouble eliminating (B).

Here is what I got from the stimulus:
(T=Trust; MEC=Meaningful emotional connection; I=Isolated;H=Happiness)


/T-->/MEC-->I
--------
H--->T

Take the contrapositive from the premises and you get this:

/I--->MEC-->T
--------
H--->T


Why wouldn't (B) work? (B) says "MEC--->H" which attaches the premise to the conclusion.

[wizzard880]

Can someone help me out with "essential" in formal logic? Isn't essential a necessary condition indicator? So why is the conclusion not "T-->H"?

[amil91]

I am having trouble eliminating (B).

Here is what I got from the stimulus:
(T=Trust; MEC=Meaningful emotional connection; I=Isolated;H=Happiness)


/T-->/MEC-->I
--------
H--->T

Take the contrapositive from the premises and you get this:

/I--->MEC-->T
--------
H--->T


Why wouldn't (B) work? (B) says "MEC--->H" which attaches the premise to the conclusion.

To put it very simple I'm going to change your variables to A, B and C. MEC = A, T = B, and H = C:
If A -> B
If A -> C
------------
If C -> B
This is not a valid inference.
For example, let's say A is I have $40, B is I can afford the sweater, C is I can afford the watch. So the conclusion is saying if I can afford the watch then I can afford the sweater. What if the sweater cost $40 and the watch cost $39?

Back to the actual stim, we need something that gets us from H to T. We know from the premises that NOT I gets us to T, so if H gets us to NOT I then it will also get us to T from a simple logic chain.

Can someone help me out with "essential" in formal logic? Isn't essential a necessary condition indicator? So why is the conclusion not "T-->H"?

You are correct that essential indicates a necessary condition, but you have them reversed in your T then H statement. The statement after the 'then' is the necessary condition: If H then T. Think of it like this, since trust is essential to happiness, if someone is happy, they absolutely must have, without a shadow of a doubt trust as it is 'essential' to happiness. But having trust does not guarantee happiness.

[testtakernce]

Nice work ilona11223344! That's exactly right.

for WITHOUT trust there can be no meaningful emotional connections to another human being.
~EC--->~T
because WITHOUT is a necessary condition indicator. I don't understand how trust, which follows after "without" is a sufficient condition?

You have it correctly that trust is a necessary condition, but you also need to keep in mind that for every conditional relationship, there is also the contrapositive.

So if we can set up the statement WITHOUT trust there can be no meaningful emotional connections to another human being as:

EC ---> T

we can rephrase this as:

~T ---> ~EC

I am so confused on the statement "for without trust there can be no meaningful emotional connection to another human being and without meaningful emotional connections to others we feel isolated"

You diagrammedu] EC ---> T[/u]

But I diagrammed it as : ~EC ---> ~T

I chose to do it this way because the "without" negates the sufficient, and the "no" in the phrase "no meaningful emotional connection to another human beings" negates the necessary, creating

~EC ---> ~T

Should the two negatives have just canceled each other out?

Why am I wrong, please let me know!

[mikaeldubinsky]

Here are the premises
H=Happiness
M= Meaningful Blah Blah Blah
T= Trust
I= Isolated

M ---T
~I----M
The Conclusion H----T

Lets start at the Premises. Eliminate both M's to arrive at ~I----T
Now we are left with the Conclusion: H---T

Eliminate Both T's to Arrive at H--- ~I
The contrapositive of course is I---- ~H Exactly what B says: "No one who is feeling isolated can feel happy"

[courtney_chrusch]

Can someone please explain why the first sentence is translated at H --> T? And to explain further what Matt said about "knowing trust does not guarantee that you have happiness?" That does not make sense to me

[ohthatpatrick]

Conditional logic is the idea that certainty flows from one idea (the left side trigger) to the second idea (the right side consequence).

I could say
"If you're in Los Angeles, you're [certainly] in California."

LA --> CA

You can NOT read that backwards with certainty.

If I tell you that Joe is in CA, you cannot with certainty say that Joe is in LA.

In Matt's language
"knowing someone is in CA does not guarantee that they are in LA"

That's what Matt was saying, when he said
"knowing trust does not guarantee that you have happiness?"

We have a conditional that says
If you have happiness, you [certainly] have the ability to trust other people.
H --> T

If I say "Joe trusts other people", we still don't know whether or not he's happy.

A more real world example:
"The ability to pass a written test is essential to getting a driver's license".

If you have a driver's license, I am certain you were able to pass the written test.
DL --> passed written

But if I say "Joe passed the written test", I don't know whether or not he got his driver's license (maybe he failed the driving test).

Frequently on LSAT, an author will mention one thing as a requirement to get something else.

Having X is essential to getting Y.

They try to trick you into going along with the idea that "once you have X, you have Y".

That's where conditional logic's cold, mathematical nature helps us.

Meeting one prerequisite doesn't guarantee me you reach the finish line.
But having met the finish line guarantees me that you met a prerequisite.

So we diagram the first claim as
Happiness --> able to trust others
because (the contrapositive)
"if you WEREN'T able to trust others, you couldn't be happy."
Trusting others is ESSENTIAL, so without it, you're screwed.

There are four main categories of conditional certainty:
RULES/CONDITIONS: if, when, whenever
UNIVERSALS: all, any, each, every, no, none, never
GUARANTEES: ensures, leads to, inevitably results in
REQUIREMENTS: only, only if, requires, depends on, essential, must, etc.

When you see a conditional, like A --> B, you can choose to read that as
If A, then B
All A's are B's
A inevitably results in B
A requires B

One cheap trick is to remember that Required things go on the Right side.

So when you see trusting other is essential, think "trust is required, so trust goes on the right side"

[hnadgauda]

It usually takes me a very long time to diagram LR Sufficient Assumption questions. I did this question much faster using the following reasoning:

Conclusion: H-->TP

New term is H (happiness).

Analysis of answer choices:

A: I-->~H; has H on necessary side and is negated; contrapositive--correct!
B: EC--> H; has H on necessary side; reversal--eliminate!
C: eliminate; doesn't contain new term, H.
D: ~I-->H; has H on necessary side; reversal--eliminate!
E: eliminate; doesn't contain new term, H.

Is this a valid way to answer sufficient questions that can be diagrammed?

[KendallW586]

I am missing the link. How on earth do you end up linking H with I?

[HughM388]

The test, understandably, wants test our ability to connect all the premises to the conclusion, as in (A); but my understanding of conditional logic is such that I remain uncertain if you could jump the chain and insert "happiness" closer to "trust," by creating complete overlap between the set of "emotional connection" and "happiness," as (B) would begin to do.

If (B) instead said something like "Anyone who has a meaningful emotional connection is happy" would there not be complete overlap between "emotional connection" and "happiness" such that "happiness" was then also sufficient for "trust?"

~isolated --> emotional connection (=happiness) --> trust

To test my own understanding of the conditional chains I often try to wedge elements into places in the chain where the question didn't intend them to go, but I'm not sure if I'm doing it legitimately.

[WilliamS670]

There's a lot of discussion of the appropriate logic chain, so this could be redundant. Briefly though:

Everything before the first comma gives us H--->T. That's the conclusion, the truth of which we want to trigger with one of the answer choices, when combined with the rest of the stimulus.

After that first comma, our chain begins as ME--->T, and -ME--->I...

...and then combines to -T--->-ME---->I.

Answer choice (A) gives us I---->-H...

...which, when combined with the chain, gives us: -T--->-ME--->I--->-H...

...and this, when reversed, gives us H--->T, the conclusion of the stimulus.