True, hence we did not transform, but replace the quantifier. The original statement "all people are not trained" was false and we wanted to make a true stateme

True, hence we did not transform, but replace the quantifier. The original statement "all people are not trained" was false and we wanted to make a true statement. There are people who are trained, thus we say "there exist people who are not trained", which allows us to say "there exist people who are trained". Of course, this is not an equivalent statement to the original statement.