Given,
The focal length of the concave mirror, f=10 cm
The object distance, o=5 cm
From the mirror formula, we have,
[tex]\frac{1}{f}=\frac{1}{o}+\frac{1}{i}[/tex]Where i is the image distance.
On substituting the known formula,
[tex]\begin{gathered} \frac{1}{10}=\frac{1}{5}+\frac{1}{i} \\ \Rightarrow\frac{1}{i}=\frac{1}{10}-\frac{1}{5} \\ =-\frac{1}{10} \\ \Rightarrow i=-10\text{ cm} \end{gathered}[/tex]And the magnification is given by,
[tex]m=\frac{-i}{o}[/tex]On substituting the known values,
[tex]\begin{gathered} m=\frac{-(-10)}{5} \\ =2 \end{gathered}[/tex]Thus the object is not diminished, it is magnified.
Thus the given statement is false.