Sufficient & Necessary Questions Question 39

If there are any inspired performances in the concert, the audience will be treated to a good show. But there will n...

aliH on November 5, 2020

“Unless” S&N

Hello! I got to the correct conclusion and answer in the wrong way. I diagrammed GoodShow—>SophsicatedListener instead of doing /SL—>/GS, which is what the answer’s explanation laid out. I get that I diagrammed the contrapositive correctly and that’s why I was able to conclude correctly, but I’m nervous that I will do this again and lead me to the incorrect diagram/answer. I thought “unless” introduced Necessary and then negate the other part of the statement and make is Sufficient, but that’s not how the explanation was diagrammed. It was diagrammed. Can you help explain this?

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SamA on November 7, 2020

Hello @aliH,

You did not do anything the wrong way here. Remember that a contrapositive carries the exact same logic as its counterpart.

Let's look at the sentence in question: "There will not be a good show unless there are sophisticated listeners in the audience."

If you follow the formula you described, the diagram will look like this:
GS ---> SL
That is how I diagrammed it as well. However, it is totally acceptable to diagram it like this:
no SL ---> no GS

They are interchangeable, and both are correct. This will not lead you to the wrong answer, as long as you diagram properly. If you are doing a parallel reasoning or flawed parallel reasoning question, then you should pay attention to if and how a contrapositive is used. In this context, you were totally correct.