The statement is false.
Work Step by Step
A cation is formed from a neutral atom when at least one electron is removed from the occupied atomic orbitals. When a cation is formed, the nuclear charge of the atom stays the same. However, now since electrons have been removed, there would be less electron-electron repulsions among the electrons. Therefore, the effective nuclear charge would be larger to any electrons. In other words, the electrons left are more attracted to and move closer to the nucleus, making the radii of the cations smaller than the corresponding neutral atoms. The statement is false.