Q9 - Some people are Montagues

[iridium77]

The first line of this stimulus is, I think, meant to be perceived as accounting for all possible conditions in that all people are understood to be either Montagues or Capulets. I just realized, though that this is not a required condition in order for E.) to be right...

Capulet--->~Montague
~Montague--->Intemperate
ergo:
Capulet--->~Montague--->Intemperate
ergo:
Capulet--->Intemperate

...Right ?

[timmydoeslsat]

I disagree that the first statement is telling us that all people are either M or C.

We can have people not be M or C and it is perfectly consistent with this stimulus.

To say that some people are M and some people are C does not preclude others from being something other than M and C.

[olenaschirripa]

Is there any chance for someone to explain this question in detail.
Thanks

[timmydoeslsat]

An unsual question type, but this contains material that can show the importance of reading through logical statements quickly.

There are numerous ways to approach this must be true question.

In this case, you could literally say "People some M" "People some C."

I personally would just notate that we have situations "M" and "C" occurring.

The next statement can be shown as:

M ---> ~CL

And the next:

C ---> CL

And in an unsurprising revelation, the argument concludes:

C ---> ~M

We are then given two more statements with one being in the question stem itself.

Last statement in stimulus: ~M ---> I

Information in question stem: M ---> ~I

Which can be shown as a biconditional arrow: M <---> ~I

or...~M<--->I....it conveys the exact same meaning.

(To answer this question, you did not even need the information supplied by the question stem.)

So this is what we have in total:

M ---> ~CL
M <---> ~I
___________
C ---> ~M

When you negate one side of a biconditional arrow, you must negate the other. So we can make an inference with the conclusion reached in the stimulus. We can go from ~M ---> I, by combining the last premise in the argument to the conclusion in the argument.

So we have C --->~M--->I

This is what answer choice E states. All C's are I's.

[olenaschirripa]

Now it's clear, thank you. I just have question as to biconditional arrow. You said:


[quote="timmydoeslsat"]

When you negate one side of a biconditional arrow, you must negate the other.


are you talking about contrapositive there or it's something else?

[timmydoeslsat]

It is that exactly. It is nothing more than the idea of eliminating the necessary condition of a statement, which will then eliminate the sufficient condition of a statement.

When we have a one way arrow...

A ---> B

And you negate the necessary...you must then negate the sufficient.

When you have a two way arrow...

A <---> B

Both sides of the arrow function as necessary conditions and sufficient conditions. So if you negate one side, you are automatically negating a necessary condition, which in turn implies the sufficient is eliminated as well. So you then must eliminate the other side as well.

[giladedelman]

Nice explanation!