Quantifiers Questions - - Question 16

No small countries and no countries in the southern hemisphere have permanent seats on the United Nations Security Co...

AnnaC October 1, 2019

Why was the "and' broken up in two different sentences?

I thought that each time a sentence / premise is given with the word "and", you're supposed to lay it out in the if - then format of "A and B ---> C" but I see that this was in this example it was diagramed as follows: A ---> C B----> C

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Irina October 1, 2019

@AnnaC,

I am assuming you are referring to the sentence "No small countries and no countries in the Southern Hemisphere have permanent seats," since this is "No" statement, a proper way to diagram it would be:

A v B -> ~ C
If it a small country or a country in SH THEN it is not on the SC

Which is logically equivalent to:

C-> ~A & ~B

IF a country is on the SC THEN it is neither a small country nor in the SC

While it is not wrong to diagram it as:

A -> ~C
B -> ~C

This notation would essentially be skipping a step and making an inference from:
A v B -> ~ C .

It is ultimately a matter of personal preference and your level of comfort with the rules of inference, I think using a compound statement form is more visually intuitive but it is not wrong to diagram it either way.

Let me know if you have any further questions.