Sufficient and Necessary Question

[ellenb]

Dear Powerscore,

It was mentioned here in the book on page 2-10 (lesson 2) that it is possible to link two sufficent and two necessary conditions? could you show an example of each.

Thanks

Ellen

[Dave Killoran]

Hi Ellen,

Sure, we're happy to help! That statement just means that the test makers can link any condition, and it doesn't have to be an a nice orderly A B C chain like the one under discussion in that section of the lesson. So, for example, they could decide that two statements are connect through a common sufficient condition, such as in:

A B
A C

(I'd actually diagram that without the two separate As (with both arrows coming out of that single A), but that is hard to do under the constraints of the forum!). As a reference, from the statements above, the inference that can be drawn is that "some Bs are Cs."

Or, they could link two statements through a common necessary condition, such as in:


C D
B D

(Again, I'd actually diagram that without the two separate Ds (with the two arrows pointing at the single D), but the diagramming limitations of the forum make that difficult). Just fyi, there is no inference that can be drawn from the statements above.

Please let me know if that helps. Thanks!

[ellenb]

I like your last point, I actuallly drew a ven diagram to see it better.

So, if we have all B cointained in D and all C contained in D, then the circle of B and the circle of C might not even have to cross, D could be just one big circle correct? It would be difficult to draw it in here. But, I want to make sure that I have the right thought process as far as why we cannot have B some C.

Thanks a lot!

Ellen

[Dave Killoran]

Yes, you are correct: B and C could overlap in that big D circle, but they don't have to overlap.

And for anyone else reading, we don't advocate using Venn diagrams to solve LSAT LR questions (see http://www.powerscore.com/lsat/help/venn_limits.cfm for our view of Venn on the LSAT), but for explanatory purposes in situations like this it can be helpful.

Thanks!

[ellenb]

So, if I were not to use ven diagrams what is the reason/explanation that I cannot make a D some C statement?
Thanks for keeping up with my questions!

Regards,

Ellen

[Dave Killoran]

Hey Ellen,

That revolves around the entire basis for how conditional statements connect, and all the explanations behind this theory are in the Formal Logic section of the Online Student Center, specifically under the Lesson 8 header. It's explained in great detail there!

Thanks!

[Nikki Siclunov]

Ellen,

Let's take Dave's second hypothetical and examine its implications:

C D
B D

B and C don't need to overlap: if all cats are animals (C A) and all dogs are animals (D A), does it follow that some cats are dogs? Of course not. There is no connection between C and B other than the fact that they share a common necessary condition (D in the example above with arrows, A in my Animals example). This, in and of itself, does not guarantee that some C are B (or vice versa). Of course, it is possible that they are - but we cannot know that based solely on the above-mentioned statement.

[ellenb]

Nikki,

Did you mean that they have A in common? I lost you there for a bit

So did you mean,

D-->A
C--->A

and because they have A in common (both are animals) does not mean that it has to be true that some dogs are cats.

What about,

A--->C

A--> D

Here I can conclude that some Cats are Dogs( an implausible statement), but based on the diagram, it should be right, correct? So, I can conclude a some statement when I have a common sufficient condition and not when I have a common necessary condition?

Thanks

Ellen

[Dave Killoran]

Hi Ellen,

Yes, you are correct on both counts. And Nikki edited his post for clarity about "A" so check that out too.

Thanks!