1953 AHSME Problems/Problem 40

Problem

The negation of the statement "all men are honest," is:

$\textbf{(A)}\ \text{no men are honest} \qquad \textbf{(B)}\ \text{all men are dishonest} \\ \textbf{(C)}\ \text{some men are dishonest}\qquad \textbf{(D)}\ \text{no men are dishonest}\\ \textbf{(E)}\ \text{some men are honest}$

Solution

Note that $\textbf{(A)}$ and $\textbf{(B)}$ are the same, and $\textbf{(D)}$ is the same as the quote in the statement "all men are honest" (that we have to found its negation). If not all men are honest, then that means that there is at least 1 dishonest (could be just one that spoils it for all the rest, or 5, for one, we definitely can't say it's all of them who are dishonest). So: $\boxed{\textbf{(C)} \text{some men are dishonest}}$ .

1953 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 39	Followed by Problem 41
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1953 AHSME Problems/Problem 40

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