1960 AHSME Problems/Problem 10

Problem 10

Given the following six statements: $\text{(1) All women are good drivers}$ $\text{(2) Some women are good drivers}$ $\text{(3) No men are good drivers}$ $\text{(4) All men are bad drivers}$ $\text{(5) At least one man is a bad driver}$ $\text{(6) All men are good drivers.}$

The statement that negates statement $(6)$ is:

$\textbf{(A) }(1)\qquad \textbf{(B) }(2)\qquad \textbf{(C) }(3)\qquad \textbf{(D) }(4)\qquad \textbf{(E) }(5)$

Solution

We can obviously see that statement $3$ contradicts statement $6$ since it says that all men are not good drivers while statement $6$ says they are. So the answer is $\boxed{C}$

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1960 AHSME Problems/Problem 10

Problem 10

Solution