- The assertion (A) is false because while it is true that a plane mirror cannot produce a real image, a convex mirror can produce virtual images but does not produce real images under any circumstance. Thus, the assertion is incorrect.
- The reason (R) is also false. A virtual image formed by one mirror can indeed serve as an object for another mirror, and a real image can be formed by using this object. Thus, the statement that a virtual image cannot serve as an object for producing a real image is also incorrect.
Therefore, the correct answer is:
\[
\text{(D) Assertion (A) is false and reason (R) is also false.}
\]