Question

K+ ions are smaller in size than k. true/ false???

Answer 1

True
When a Potassium atom becomes a Potassium ion, it looses a single electron to become K+. 
The one electron it looses is located in its outermost, valance, electron shell (the S orbital). 
When this electron is taken away, the S orbital is empty and the radius of the resulting ion is now smaller than the previous atom.