No, people should not live together before marriage. It is true that once people live together, most of them will find each others shortcomings, which are not easily noticed no matter how much they love each other. Therefore, many marriage comes to end because of this problem. However, if people live together some time before marriage to find out they are right for each other to enter into marriage, they are more freely to break up for less serious matter and then will be at risk of not finding real partner which could be earned through bearing each other with not only love but endurance.