Note to self: lexicographic ordering

The following (pseudo-C++) code is the correct way of writing lexicographic "less than" function for the tuple of two items:

bool less_than(const pair &p1, const pair &p2)
{
  if(p1.first == p2.first)
    return p1.second < p2.second;
  return p1.first < p2.first;
}

This code cannot be rewritten using only boolean operators. My mistake was writing

return
  (p1.first < p2.first) ||
  (p1.second < p2.second);

This does not work! Analogous combination with && also doesn't work. It could be rewritten to use the ?: operator, but with doubtful benefits. Note to self: don't try being too smart again!