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Difference between revisions of "1962 AHSME Problems/Problem 30"
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As long as the statement isn't p and q are both true, it satisfies the negative, so 2, 3, and 4 work, yielding an answer of 3, or \textbf{(D)}.
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As long as the statement isn't p and q are both true, it satisfies the negative, so 2, 3, and 4 work, yielding an answer of 3, or <math>\textbf{(D)}</math>.

Revision as of 21:08, 1 April 2020

Problem

Consider the statements:

$\textbf{(1)}\ \text{p and q are both true}\qquad\textbf{(2)}\ \text{p is true and q is false}\qquad\textbf{(3)}\ \text{p is false and q is true}\qquad\textbf{(4)}\ \text{p is false and q is false.}$

How many of these imply the negative of the statement "p and q are both true?"

$\textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 4$

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

As long as the statement isn't p and q are both true, it satisfies the negative, so 2, 3, and 4 work, yielding an answer of 3, or $\textbf{(D)}$.

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