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

Rebecca on October 20 at 06:23PM

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!

1 Reply

Irina on October 21 at 01:42AM


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.