For any natural number n, it is possible to construct a stable matching problem input instance with n hospitals and n students, such that there is a feasible solution assigning all hospitals and all students to their last choices. 

Consider an instance of the Stable Matching Problem in which there exists a hospital h and a medical student s such that h and s are ranked last on each other’s preference list. Then, no stable matching of this instance can include the pair (h,s). 

For any natural number n, it is possible to construct a stable matching problem input instance with n hospitals and n students, such that there is a feasible solution assigning all hospitals and all students to their first choices. 

Consider an instance of the Stable Matching Problem in which there exist n hospitals to be matched with n medical students. Gale-Shapley algorithm guarantees that fewer students than hospitals are matched to their first choices. 

Consider the following preference tables for three university hospitals and three medical students.    1st  2nd 3rd DUKE Cam Ada Bea NYU Ada Cam Bea UIUC Cam Bea Ada           1st 2nd 3rd Ada DUKE UIUC NYU Bea UIUC DUKE NYU Cam UIUC NYU DUKE (i) Which of the following is the output of the Gale-Shapley algorithm? [GaleShapley] (ii) Which of the following is a stable matching that assigns each student to their best valid partner?[StudentBestMatching] (iii) Which of the following is an unstable pair with respect to the matching (DUKE-Ada, NYU-Cam, UIUC-Bea)?[UnstablePair] (iv) Which student (if any) can improve his/her/their match in the Gale-Shapley output by lying? [TrickingTheAlgorithm] 

The unit designed for the cremation process is called the: 

Experience driven consumers are willing to pay for an experience they feel is meaningful 

Cremated human remains are defined as: 

Communities with a large portion of the population that is mobile and has less connection to their geographic origins have a higher cremation rate. Select the best term for this type of community. 

The process of reducing a dead human body to bone fragments using flame is defined as:  s and extreme heat