Two statements are given—one labeled Assertion $(A)$ and the other labeled Reason $(R)$. Select the correct answer to these questions from the codes $(a)$, $(b)$, $(c)$, and $(d)$ as given below:
$(a)$ Both $A$ and $R$ are true, and $R$ is the correct explanation of the assertion.
$(b)$ Both $A$ and $R$ are true, but $R$ is not the correct explanation of the assertion.
$(c)$ $A$ is true, but $R$ is false.
$(d)$ $A$ is false, but $R$ is true.
Assertion $(A)$: We can decide the nature of a mirror by observing the size of the erect image formed in the mirror.
Reason $(R)$: The minimum distance between a real object and its real image in a concave mirror is non-zero.

(N/A) $1$. Assertion $(A)$: By observing the size of an erect image, we can identify the mirror. For a plane mirror, the size of the image is equal to the object $(m=1)$. For a convex mirror, the erect image is always diminished $(m<1)$. For a concave mirror, the erect image is always magnified $(m>1)$. Thus, the assertion is true.
$2$. Reason $(R)$: For a concave mirror, a real image is formed when the object is placed beyond the focus $(u > f)$. The real image and the object coincide only at the center of curvature $(u = v = 2f)$. At this point, the distance between the object and the image is zero. Therefore, the statement that the minimum distance is non-zero is false.
$3$. Conclusion: Since $A$ is true and $R$ is false, the correct option is $(c)$.