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# CRB P117, #6 - Diagramming Unless

PowerScore StaffJoined: 09/02/2017Posts: 1
Yesterday, I received the following question:

Hi Team,

First of all, I would like to congratulate for writing such a thorough book. It's very helpful.  That being said, I would like to bring in you attention a potential mistake in the answer of sufficient and necessary diagram drill ques on page no 117, drill no 6 of 2017 edition.  It says : Maria will not speak during the meeting unless the chairman does not speak.    While as per me the answer should be : if Maria speaks during the meeting, then the chairman will also speak during the meeting.    But the answer given in book is : if Maria speaks during the meeting, then the chairman will not speak during the meeting.    Please clarify.

Hi,

Thanks for the question, and for the kind words about the book—I greatly appreciate them! Ok, let's take a look at your question. First, the good news is that the book is correct J  The drill answer is accurate, and in your translation you made a small error with the necessary condition that caused you to arrive at the wrong diagram. So, let's talk about how to handle this statement, and I think afterwards you won’t ever miss a question in this vein again.

First, let me introduce you to a neat trick to handle statements involving terms like “unless” and “except.” It’s called the Unless Equation:

The Unless Equation

In the case of “unless,” “except,” “until,” and “without,” a special two-step process is applied to create the diagram:

1. Whatever term is modified by “unless,” “except,” “until,” or “without” becomes the necessary condition.

2. The remaining term is negated and becomes the sufficient condition.

In the Unless Equation, the first step reads as follows: "Whatever term is modified by “unless,” “except,” “until,” or “without” becomes the necessary condition." In our drill, "unless" modifies: "… the chairman does not speak”, which would be CS. So, we’d have the following diagram thus far:

Sufficient --> CS

Then , the  remaining term is negated and becomes the sufficient condition. The remaining terms i: “Maria will not speak…” which would be diagrammed—when negated—as MS. That leaves us with a diagram of:

MS --> CS

That’s the same diagram as in the book, so it is correct.

In your diagram, you removed the existing negative on the necessary condition, leading to the problem. If you memorize the Unless Equation above, you won’t make the same mistake again (and, also look at all the other drill items there with one of the four terms (unless, until, etc), and you will see how they all work the same way).