Sufficient & Necessary Questions - - Question 10

Because of the recent transformation of the market, Quore, Inc., must increase productivity 10 percent over the cours...

ritagentile May 14, 2020

Question 10

Hi, I watched the explanation video and now understand how to diagram for the answer. I was initially confused, however, and still am confused about the word "possible" and "attainable" because to me these words imply possibility and not FACT that this is what will happen. So why can we say IncreaseP10%---> IncreaseP20% if these are just possibilities? It says the company MUST increase P by 10% in order to not go bankrupt, so why would the possibility of increasing P 10% matter here?

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SamA May 14, 2020

Hello @ritagentile,

I understand your confusion, because we have some different language in these two premises. The first is certain. If the company does not increase productivity by 10%, then it will certainly go bankrupt.

not BR ------> 10%I
not 10%I -------> BR

There is an element of "possibility" in the second premise. If a 10% increase is possible, then so is a 20% increase.

10%P ------> 20%P
not 20% P ------> not 10%P

The language is different, but there is a way to connect these premises. If a 10% increase is not possible, then we can conclude that a 10% increase won't happen, which will lead to bankruptcy. Similarly, if a 10% increase happens, we can confirm that it is indeed possible, and therefore so is a 20% increase. So, we can connect the premises like this:

not 20%P ----> not 10%P -----> BR
or its contrapositive
not BR ------> 10%I ----> 20%P

ritagentile May 26, 2020

this makes much more sense now! Thanks a lot!