Need someone to explain why splitting 'or' sufficiency is okay

markmywords

In the lesson about and/or sufficiency splits, JY says we split the 'or'. But in another lesson we learn that two sufficient conditions pointing to one necessary is an invalid argument. So i'm confused why it's okay to split the 'or' sufficiency. Can someone please dumb that down for me?

scottie007

If A or B, then C:
A or B-> C

Think about what we know if it is A. If we know it is A, then we know it is C.
A-> C

What about if we know it is B? If we know B, then we know it is C.
B-> C

See how we have split the original conditional statement (If A or B, then C) into two separate statements. A-> C ; B-> C

It might work better to show this using a real life example which holds true.
Ex: If it's a cat or a dog, then it's a mammal. D or C -> M

From your intuition you would know when you see a cat, you know it's a mammal.
C-> M

And the same for a dog: D-> M

Once again we see that the logic still holds from the original statement, we are just able to break it into two statements because of the "OR"

I'm not familiar with your comment about not being able to have 2 SCs pointing to 1 NC, but it is certainly the case that "OR" presented in the sufficient condition can be split into two logical statements, with each component of the "OR" statement pointing to the same necessary condition.

Essentially the OR presents two independent elements, either of which are sufficient for the necessary condition, and because each are sufficient on their own to prove the necessary, each element can be represented individually as it's own statement to prove the necessary.

As opposed to AND statements in the sufficient condition, where the elements are dependent on each other co-existing to prove the necessary.

This is my first time responding to one of these but let me know if you have any questions, hopefully that was able to help some.