AHSME 1962 Problem 30

Consider the statements: $\textbf{(1)}\ \text{p and q are both true} \textbf{(2)}\ \text{p is true and q is false} \textbf{(3)}\ \text{p is false and q is true} \textbf{(4)}\ \text{p is false and q is false.}$ How many of these imply the negative of the statement "p and q are both true?" $\textbf{(A)}\ 0 \textbf{(B)}\ 1 \textbf{(C)}\ 2 \textbf{(D)}\ 3 \textbf{(E)}\ 4$