Positive ions are smaller than the atoms from which they are formed, but negative ions are larger than the atoms from which they are formed.

True. Positive ions are formed when atoms lose electrons. The net attractive force of the greater number of protons in the nucleus is spread among fewer negatively charged electrons...therefore, the electron cloud 'shrinks' and pulls them closer to the nucleus - reducing the diameter of the atom.

Negative ions are formed when atoms gain electrons. The net attractive force of the protons in the nucleus is 'diluted' when spread among a greater number of electrons, and the electron cloud expands a bit - giving the atom a larger diameter.