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

This statement can also be written as "If someone is a man, then they are honest."

The negation of this statement is "If someone is a man, then they are not honest."

The statement that means the same as the statement above is $\boxed{\textbf{(B)} \text{all men are dishonest}}$

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1953 AHSME Problems/Problem 40

Problem

Solution