Logical Reasoning Question: PrepTest 19 Section 2 Question 17 #help

popcorn11201

Hello. I'm having trouble understanding why Answer Choice A is incorrect and why choice C is correct. Answer Choice A reads, "Whenever a society has plentiful resources, some members of that society devote themselves to the study of natural processes." In the stimulus, you know that people have leisure when they have plentiful resources, and leisure is needed for the study of natural processes. Therefore, whenever a society has plentiful resources, people have the leisure they need to devote themselves to the study of natural resources. That is why I thought Answer Choice A is correct and can't see why it is incorrect. I watched JY's video explanation, but I got lost and confused when he explained the order of logic.

I'm also having trouble understanding what part of the stimulus gives support to Answer Choice C.

If someone can please explain to me how my way of thinking about Answer Choice A is wrong and why Answer Choice C is actually correct, I would greatly appreciate it. Thank you so much in advance!

help

thinkorswim

Hi! The reason why A is wrong is due to a mistaken translation. So let's map it out together :

1) devote themselves to the study of natural processes ---> leisure
2) resources plentiful ----> leisure
3) but wait..... it also says NOT when resources are scarce so ... resources plentiful ---> leisure

its actually a bi conditional if we chain up (2) (3)

So we get :

devote themselves to the study of natural processes ---> leisure <--------> resources plentiful

In answer choice A ) we get plentiful resources <--some -> devote themselves to natural processes.
Remember this is a mistaken inference and we cannot go backwards from the some arrow all the way back to the study of natural processes. This is an invalid inference

In answer choice C ) agriculture first began in societies that have plentiful resources. How do we know this? Because in the conclusion it says these discoveries were the result of " the active study of natural processes ". If we knew we had the time to study the natural processes then we must have had leisure and THEREFORE must have had plentiful resources.

thinkorswim

One more thing just in case you were wondering why its an invalid inference :

This is a valid inference A <---s---> B ---> C . Then you can say A some C. When the some or most is at the end of the chain we cannot go the other way. So for example A ---> B <----s---> C . You cannot say that some C's are A .

popcorn11201

@thinkorswim said:
Hi! The reason why A is wrong is due to a mistaken translation. So let's map it out together :

1) devote themselves to the study of natural processes ---> leisure
2) resources plentiful ----> leisure
3) but wait..... it also says NOT when resources are scarce so ... resources plentiful ---> leisure

its actually a bi conditional if we chain up (2) (3)

So we get :

devote themselves to the study of natural processes ---> leisure <--------> resources plentiful

In answer choice A ) we get plentiful resources <--some -> devote themselves to natural processes.
Remember this is a mistaken inference and we cannot go backwards from the some arrow all the way back to the study of natural processes. This is an invalid inference

In answer choice C ) agriculture first began in societies that have plentiful resources. How do we know this? Because in the conclusion it says these discoveries were the result of " the active study of natural processes ". If we knew we had the time to study the natural processes then we must have had leisure and THEREFORE must have had plentiful resources.

Why can't you point the arrow from leisure back to the study of natural resources? Why can you point the arrow both ways between leisure and resources plentiful? Also, I'm not sure what you mean when you put some in between plentiful resources and devote themselves to natural processes. Sorry, I'm starting to get a better understanding, but I'm still not all the way there.
Thanks for your time and help!

thinkorswim

For your first question: All swans are black. This would be the translation swans ---> black. Does this mean that all black things are swans ? This is a sufficiency/necessity confusion. The reason is because the arrow only goes one way.
https://7sage.com/lesson/valid-argument-form-1-of-9/

For your second question : The reason why we can point the arrow both ways is because we know that 1) resources plentiful ---> leisure from the statement "people have leisure when resources plentiful". 2) /resources plentiful ----> /leisure from the statement "not when resources are scarce".

The reason it goes both way is because if you take the contrapositive from statement 2) we get leisure ---> resources plentiful. Therefore (1) and (2) makes it both ways.

For your third question :
https://7sage.com/lesson/valid-argument-form-4-of-9/

You really need to go back to the core curriculum and understand the section labeled "some and most relationships" JY explains it a lot better than I can typing it to you here.