The statement is: If α is one-to-one and β is onto, then βoα is one-to-one and onto. One-to-one is injection, onto is surjection, and being both is bijection. After showing that the statement is false, the contrapositive was asked for. The answer given is: If βoα is not one-to-one and onto, then α is not one-to-one or β is not onto. They changed the "and" to an "or." I was thinking that the "and" would be conserved in the contrapositive statement. Is it valid or necessary to change an "and" to an "or" for contrapositive statements?