1962 AHSME Problem 30

Consider the statements:

\begin{array}{l} \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.} \end{array}

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.