Use
Format | Conditional Format
set the Cell Value parameter to "equals" and select FALSE from the list for
the value to equal. Then set the font color to the same color (white?) as
the background of the cell itself. It actually still prints, but because
it's white-on-white or color-on-color, then it doesn't appear on the printed
output.
This presents a problem if you actually want to see the word FALSE while
viewing the screen, of course.