Refer to the sequence of Stirling numbers of the second kind. If X is a set with n elements and Y is a set with m elements, express the number of onto functions from X and Y using Stirling numbers of the second kind. Justify your answer.
a) S(n,m)
b) S(m,n)
c) S(n,m)⋅S(m,n)
d) S(n,m)+S(m,n)
