Quantifiers Questions - - Question 16

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

isabella April 21, 2020

diagramming

Why is the first sentence diagrammed as two separate conditions while the second sentence is diagrammed as one, indicated by the "&" sign? I diagrammed the first one as SC & SH --> not PS instead of separating it. I did end up getting confused because of the combination, so does it matter if they are together or separate?

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SamA April 26, 2020

Hello @isabella,

The problem with your diagram is not that you combined the two conditions. The problem is that you used "&" instead of "or." The correct diagram of the first sentence is this:

SC or SH ---> not PS

it is also acceptable to separate them.

SC ---> not PS
SH ---> not PS

When we have an "or," it means that just one of these sufficient conditions will bring about the necessary. This is why we can write them separately. However, you cannot cannot do the same with an "and" statement.

I understand your confusion, because the first sentence does include the word "and." However, you created a diagram of this sentence: "Any small country that is in the southern hemisphere does not have a permanent seat." This would be represented by:
SC and SH ---> not PS
it is not appropriate to separate this into two statements, because we can't make a conclusion based on one of these conditions alone.