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[GMAT数学] GMAT考试:Testprep数学精解2

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  If I eat nutsthen I break out in hives. This in turn can be symbolized as NH.

  Nextwe interpret the clause there is a blemish on my hand to mean hiveswhich we symbolize as H. Substituting these symbolssintosthe argument yields the following diagram

  NH

  H

  ThereforeN

  The diagram clearly shows that this argument has the same structure as the given argument. The answerthereforeis

  Denying the Premise Fallacy

  AB

  ~A

  Therefore, ~B

  The fallacy of denying the premise occurs when an if-then statement is presentedits premise deniedand then its conclusion wrongly negated.

  Example

  The senator will be reelected only if he opposes the new tax bill. But he was defeated. So he must have supported the new tax bill.

  The sentence The senator will be reelected only if he opposes the new tax bill contains an embedded if-then statementIf the senator is reelectedthen he opposes the new tax bill. This in turn can be symbolized as R~T. The sentence But the senator was defeated can be reworded as He was not reelectedwhich in turn can be symbolized as ~R. Finallythe sentence He must have supported the new tax bill can be symbolized as T. Using these symbols the argumen

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