If all of the board members are not present at a board meeting (but we have a quorum, three of five), is it true that if anyone votes "no" on an item, the motion fails?
It is confusing, and you are not alone. For a five-member board, at least three must vote yes to pass a motion, regardless of how many are present. This means that if three show up – that gives you a quorum because three of five are present – all three must vote yes to pass a motion.
If four show up for the meeting, then a vote of 3-1 will pass a motion.
If all five are present, a vote of 3-2 will pass a motion.
In each case, at least three members of a five-member board must vote yes to pass the motion, regardless of how many are present.
If you have a seven-member board, four must be present for a quorum and at least four must always vote yes for a motion to pass, regardless of whether there are four, five, six or seven members present.