Can you help me solve this problem.

2. Let U = {1,23, ...,2019} and suppose that, VS E U, we dene [S] = {X E U I S E X}, where the notation S E X means that the sets 3 and X are equinumerous. a) What is the minimum value of k, if any, for which there exists a sequence of sets 51) 5'2, , Sk such that 31 e [{1}],52 e [{1,2}],S3 E [{1,2,3}], ...,5k 5 [{1,2,3, ...,k}], and 51 u 32 U 53 U U 3k : U? Why