$15 \cdot 20$ The negation of the statement "For all real numbers $a, b$, if $a=0$, then $a b=0$" can be written as: there exist real numbers $a, b$ such that
(A) $a \neq 0$ and $a b \neq 0$.
(B) $a \neq 0$ and $a b=0$.
(C) $a=0$ and $a b \neq 0$.
(D) $a b \neq 0$ and $a \neq 0$.
(E) $a b=0$ and $a \neq 0$.
(17th American High School Mathematics Examination, 1966)
[Solution] Let $\mathrm{P}(a, b)$ be a proposition concerning $a, b$.
Then the negation of the proposition “for all $a, b, P(a, b)$ holds” is “there exist $a, b$ such that $P(a, b)$ does not hold”.
Therefore, the answer is $(\mathrm{C})$.