Formal Logic help

errrrr1452

Can someone please help me diagram and understand the inferences made from these statements?

Some As are Bs.
All Cs are Ds
No Bs are Cs.

Here is what I have so far.

AsomeB—-> ~C
~D—->~C

Inference: Asome~C

FaviPapi-1-1

Some As are Bs: As <---S---> Bs

All Cs are Ds: Cs ---> Ds

No Bs are Cs: Bs ---> ~Cs

Linking them will look something like this:

As <---S---> Bs ---> ~Cs
~Ds ---> ~Cs

(I can't find a way to connect Bs and ~Ds to ~Cs, but if you are writing this down, you should connect them...)

Anyway, the inferences are:

1. As <---S---> ~Cs
2. ~Bs <---S---> Ds

I hope this helps!

errrrr1452

@FaviPapi Thank you for the reply. How did you make the inference ~B <--s--> D? I am having trouble making that inference.

FaviPapi-1-1

Here is how you do it:

If we have these two conditional statements:

X —> Y

Z —> Y

We can’t infer anything...

However, if we take the contra-positive of those two conditional statements, we get the following:

~Y —> ~X

~Y —> ~Z

From there we can infer that ~X <—S—> ~Z

The reason behind that is the following: ~X and ~Z must share some common-ground or, as JY says, some interception because ~Y is brought into ~X and ~Z...

I hope this helps - good luck studying!

errrrr1452

@FaviPapi Thank you so much!!

FaviPapi-1-1

Of course, let me know if you have any other questions.