# Most of the mines that Moradco operates in the province of Velyena have never violated environmental regulations. Eve...

Rebecca on October 20, 2019

How to diagram the Quantifier and S->N Stmts

Hello, Can someone please explain how to diagram this question? There is the quantifier, "Most", and the sufficient/necessary statement stating "every.." but I'm not sure how to combine them to make a valid conclusion. If this question shouldn't be diagrammed, how would I find the correct answer? Thank you so much!

2 Replies

Irina on October 21, 2019

Thank you for your question. We can diagram these statements in the following way.

Velyena most->. ~ violate environmental regulations

We cannot use transposition on "most" statements but we can reverse a "most" statement to infer that:
~violate environmental regulations some-> Velyena

Some mines that never violated environmental regulations are operated by Moradco in Velyena.

Gold -> violate environmental regulations
We can infer that if a mine has not violated regulations, it is not a gold mine.
~violate -> ~ gold

We can combine both premises to conclude that:

Velyena most -> ~violate -> ~gold which is equivalent to:
Velyena most -> ~gold

Most of the mines in Velyena are not gold mines (D).

Let me know if you have any other questions.

jing jing on September 7, 2020

I am not a skilled diagrammer and I am not an instructor, but I donâ€™t think we need to diagram anything for this question.

If it is a gold mine, then it has to have violated a regulation at some point in time. Since most of the mines that Moradco operates in the province of Velyena never violated any regulations, most of the mines that Moradco operates in the province of Velyena must not be gold mines.

Is this the right logic? Please correct me if I am not correct. I never diagram anything unless I must because I am always short on time and diagramming takes too long.