Sufficient & Necessary Questions - - Question 11

Nursing schools cannot attract a greater number of able applicants than they currently do unless the problems of low ...

ankita96 May 30, 2020

Either or in question 11

When there is a "if" and an "either or" can you elaborate on why we are not applying the "if" rule and the "either or" rule. and how do we know when the "either or" rule will apply and when it will be treated as a general language

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SamA June 3, 2020

Hello @ankita96,

We are applying the either/or logic here, but it may not look exactly as you saw it in the lesson. By "either/or rule," I assume that you are talking about the process of negating one variable and making it sufficient, while the other condition becomes necessary.

For example: I will either run or or lift weights.
not R ---> LW
not LW --- R

However, the either/or as used in this question will be diagrammed differently, because it is within another conditional statement.

"If the pool of able applicants does not increase (not PAI), either the profession will have to lower its entrance standards (LES), or there will soon be an acute shortage of nurses (ASN)."

We cannot follow the process above (not LES ---> ASN). Why not? Because it is possible that the pool of applicants does increase! Our either/or statement is relevant only if the pool of applicants does not increase. In that event, we will employ the either or rule. However, we do not know what will happen to the pool of applicants. So we must represent it like this:

not PAI ---> LES or ASN
and the contrapositive
not LES and not ASN ---> PAI

If we are given (not PAI), then we can consider the either/or.
Here's an example: Let's say that the pool has not increased, and entrance standards have not been lowered.
not PAI and not LES ---> ASN

Or, let's say the pool has not increased, and there is not shortage of nurses.
not PAI and not ASN ---> LES

Can you see your standard either/or diagram here, within the larger conditional statement?
not LES ---> ASN
not ASN ---> LES

We haven't ignored the rule. I hope that answers your question, this is complicated stuff. If you can handle this, then your sufficient and necessary understanding is quite strong.

ankita96 June 9, 2020

Oh I get it, thanks a lot! This was helpful