The reason why branching cases pose a problem for personal i…

The reason why branching cases pose a problem for personal identity (synchronic [at a time] and diachronic [over time]) is because there cannot be two of the numerically identical person (while there could be two qualitatively identical persons, e.g., twins). Put differently, if person A and person B were numerically identical, they would occupy the same space-time region during the whole of “their” existence. This latter is not true in a branching case. 

Choose all the choices where the lefthand term is necessary…

Choose all the choices where the lefthand term is necessary for the righthand term. For example “Pope, Catholic” vs “Catholic, Pope.” The second combination is such that the lefthand term (Catholic) is necessary for the righthand term (Pope), but not sufficient.