Q19 - Every student who walks to school

[skapur777]

I picked D, but I circled it to signify that I didn't exactly understand why I was correct:

Some students who do not go home for lunch have part-time jobs.

I can't see how we can connect:

~HL>(some) PT

and
~HL>~WS (contrapositive of first line)

to PT>(some) ~WS

Usually I'm pretty good at this, but where did I go wrong?

HL=home for lunch
WS=Walk to school
PT=part time job

the (some) is supposed to be over the arrow but i dunno how we notate that here.

[ManhattanPrepLSAT1]

Notice that in your "some" statement

~HL>(some) PT

we can infer that some who have part time jobs do not go home for lunch. "Some" statements are reversible.

You should either put a double-headed arrow on your some statements or shouldn't put any arrow on them.

That way you can read the "some statement in reverse

~HL some PT implies PT some ~HL

When you combine a "some" statement with an "all" statement, make sure that the matching term, is located in the sufficient condition of the "all" statement. So we can combine:

PT some ~HL
~HL ---> ~WS

To arrive at the conclusion that:

PT some ~WS

You should NOT be reacting to the answer choices on a question like this one, should be predicting and then selecting the matching answer choice.

The argument is:

WS ---> HL
-----------------
PT some ~WS

We should take the contrapositive of the premise to match the term about walking to school.

~HL ---> ~WS
------------------
PT some ~WS

Then we should search for the lowest quantification possible that reflects an assumption of the argument. We can get by with adding a "some" to the evidence to arrive at the conclusion.

PT some ~HL (assumption)
~HL ---> ~WS (stated premise)
------------------
PT some ~WS (stated conclusion)

if you need help finding the assumption, let me know. And remember that since "some" statements can be reversed, answer choice (D) still represents the same idea!

[ptraye]

thanks for the explanation.

[griffin.811]

Notice that in your "some" statement

~HL>(some) PT

we can infer that some who have part time jobs do not go home for lunch. "Some" statements are reversible.

You should either put a double-headed arrow on your some statements or shouldn't put any arrow on them.

That way you can read the "some statement in reverse

~HL some PT implies PT some ~HL

When you combine a "some" statement with an "all" statement, make sure that the matching term, is located in the sufficient condition of the "all" statement. So we can combine:

PT some ~HL
~HL ---> ~WS

To arrive at the conclusion that:

PT some ~WS

You should NOT be reacting to the answer choices on a question like this one, should be predicting and then selecting the matching answer choice.

The argument is:

WS ---> HL
-----------------
PT some ~WS

We should take the contrapositive of the premise to match the term about walking to school.

~HL ---> ~WS
------------------
PT some ~WS

Then we should search for the lowest quantification possible that reflects an assumption of the argument. We can get by with adding a "some" to the evidence to arrive at the conclusion.

PT some ~HL (assumption)
~HL ---> ~WS (stated premise)
------------------
PT some ~WS (stated conclusion)

if you need help finding the assumption, let me know. And remember that since "some" statements can be reversed, answer choice (D) still represents the same idea!

Can someone write this out in words? I having a difficult time following the notations. Also how does this conclusion make sense, given the stated premise?

Thanks!

[asandova]

hi matt,

thank for the explanation! i was wondering if you could elaborate a bit..

i followed what you were saying all the way until you predicted the assumption but i think i am either not seeing it or i don't understand how "some" functions in relation to "all".

i am only on chapter 4 of the manhattan LR book, so i might not have come up any discussion of the difference yet but any clarification would be great!

edit: i actually chose the right answer, but I was guessing between A and D. i eliminated B and E because the language was too strong, and C didn't feel right.

[jrnlsn.nelson]

mattsherman's post is great -- thanks for that.

He does a nice job of explaining how to arrive at answer choice (D). Yet, I chose answer choice (A) which, in fact, is the contrapositive of the the conditional statements that include the assumption of (D).

As mattsherman posted, in order to arrive at (D) we have to see how we can get from this:

~HL ---> ~WS (the contrapositive of the first sentence)

to this:

PT (some) ~WS (the stated conclusion)

And we get there by assuming:

PT (some) ~HL

The full conditional chain can be written out as follows:

PT (some) ~HL ---> ~WS

Yet, look what happens when you take the contrapositive of this, you get:


WS ---> HL (some) ~PT


The second part of this chain:

HL (some) ~PT

is equivalent to

"Some students who do not have part-time jobs go home for lunch" -- which is answer choice (A)!


Would be super awesome if someone could clarify this.

[donghai819]

Can any teacher correct me if im wrong?

HL --some---> ~PT = PT --some---> ~HL

Some A are not B, so some B are not A

My conclusion is: this question wants to test it.

[maryadkins]

Some A are not B, so some B are not A

Correct.

I don't understand what you're saying about the conclusion, but the above reasoning is good!

[donghai819]

Hi Maryakdins,

Could you check my work is correct?

original: Most As are not B
inference: some Bs are not A

original: Some As are not B
inference: some Bs are not A

original: Most As are not C, most Bs are not C
inference: some As are B

original: Some As are not C, some Bs are not C
inference: some As are B

original: Some As are C, some Bs are not C
inference: some As are B

original: Most As are C, most Bs are not C
inference: some As are B

*original: most As are C, most Bs are C
inference: most As are B, and most Bs are A. I think this inference is wrong. If so, what would be the correct inference? some As are B?

Thanks in advance!

[maryadkins]

original: Most As are not B
inference: some Bs are not A

original: Some As are not B
inference: some Bs are not A

Correct.

original: Most As are not C, most Bs are not C
inference: some As are B

No.

We don't know the relationship between As and Bs at all.

For example, maybe most Japanese students graduate from college and most US students do as well. By your logic here, that would mean some Japanese students are US students, which is not a valid inference (and in fact, doesn't make sense). It doesn't work.

For this reason, the rest of your inferences in the post are also incorrect! When you are questioning your logic, try substituting in real life examples like I did here to catch your mistakes.

[LauraS737]

Can someone PLEASE explain why A is incorrect?

[ohthatpatrick]

You're saying that if we combine these two ideas,
All walkers goes home for lunch
+
Some non-jobbers go home for lunch
we can derive
Some jobbers are not walkers?

My initial reaction to that would be,
"How the heck could we have proven anything about jobbers? Neither one of those supporting facts says ANYTHING about jobbers?"
as well as
"How the heck could we have proven anything about not-walkers? Neither one of those supporting facts says ANYTHING about not-walkers?"

Technically, we could say the first idea, by contrapositive, allows us to say "If you DON'T go home for lunch, you're a not-walker."

But there would literally be no information whatsoever about "jobbers". So there's no way that adding (A) to the first sentence of the argument allows us to prove a statement about "jobbers".

Does that make sense?

Can you otherwise explain how you thought we could derive the conclusion by combining (A)'s idea with the "Every walker goes home for lunch" idea?

[LauraS737]

You're saying that if we combine these two ideas,
All walkers goes home for lunch
+
Some non-jobbers go home for lunch
we can derive
Some jobbers are not walkers?

My initial reaction to that would be,
"How the heck could we have proven anything about jobbers? Neither one of those supporting facts says ANYTHING about jobbers?"
as well as
"How the heck could we have proven anything about not-walkers? Neither one of those supporting facts says ANYTHING about not-walkers?"

Technically, we could say the first idea, by contrapositive, allows us to say "If you DON'T go home for lunch, you're a not-walker."

But there would literally be no information whatsoever about "jobbers". So there's no way that adding (A) to the first sentence of the argument allows us to prove a statement about "jobbers".

Does that make sense?

Can you otherwise explain how you thought we could derive the conclusion by combining (A)'s idea with the "Every walker goes home for lunch" idea?

Initially, I solved the problem like this:

All Walk --> Home for Lunch
--------------------------------------
Conclusion: Part Time Job --> Some NO Walk

Taking the contrapositive of the premise and linking it with the conclusion I got:
Some NO Home for Lunch --> Part Time Job --> Some NO Walk

I though the assumption was: Some No Home for Lunch --> Part Time Job

However, when I approached the problem by taking the contrapositive of the Conclusion instead of the premise, I got:

All Walk --> Home for Lunch
------------------------------------------
Conclusion: Part Time Job --> Some NO Walk
Contrapositive: Some Walk --> NO Part Time Job.

Some Walk --> Home for Lunch --> NO Part Time Job

HELP! WHERE AM I GOING WRONG????