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A unless B

“A unless B” is a rather complex structure. Though surprisingly we use it with little thought or confusion in our day-to-day speech.

To see that “A unless B” is equivalent to “~B—>A,” consider the following situation:
Biff is at the beach unless it is raining.

Given this statement, we know that if it is not raining, then Biff is at the beach. Now if we symbolize “Biff is at the beach” as B, and “it is raining” as R, then the statement can be diagrammed as

Example: (A unless B)

Melinda can earn an MBA unless she does poorly on the GMAT or does not get a scholarship.
Which one of the following statements cannot be validly drawn from the above statements?
  1. Melinda received an MBA. So she must have both done well on the GMAT and gotten a scholarship.
  2. Melinda received an MBA and she did well on the GMAT. So she must have gotten a scholarship.
  3. Melinda did poorly on the GMAT. So she will not earn an MBA.
  4. If Melinda does not earn an MBA, then she did poorly on the GMAT or could not get a scholarship.
  5. If Melinda does poorly on the GMAT and does not get a scholarship, then she will not earn an MBA.
This argument says that two things stand in Melinda’s way—performing poorly on the GMAT and not getting a scholarship. That is, if Melinda does well on the GMAT and gets a scholarship, then she can earn an MBA.
Since Melinda received an MBA in choice (A), she must have overcome the two obstacles—the GMAT and the scholarship. Hence (A) is valid. This eliminates (A).
Next, (B) essentially expresses the same thought as (A). This eliminates (B).
Next, (C) says that Melinda didn’t meet one of the two criteria, so she won’t earn an MBA. Hence (C) is valid. This eliminates (C).
You should notice that the conclusion in (D) is too strong. Melinda may do well on the GMAT and get a scholarship yet decide not to pursue an MBA. The answer, therefore, is (D).

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