Check all the statements that are true: A. There are functions from a set of n elements to a set of m elements.
B. If n is a nonnegative integer, then the sum of all the C(n, k) is .
C. The cardinality of a cartesian product of sets is the product of the cardinalities of the individual sets.
D. There are n! bijections from a set with n elements to itself.
E. A surjective function from a set of n elements to a set of n elements is automatically injective .
F. If a procedure can be broken down into a sequence of two tasks, and if there are n ways to do the first task, and m ways to do the second task, then there are nm ways to do the procedure.
G. If there are 2n+1 objects in n boxes, then at least one box must contain at least 3 objects.
H. If a task can be done either in one of n ways or in one of m ways, then there are n+m ways to do the task.
I. If n and r are nonnegative integers and , then C(n, r) = P(n, r)/r!.
J. Combinations C(n, r) are symmetrical in r with respect to the point .
K. An injective function from a set of n elements to a set of n elements is automatically surjective.
L. If S is a finite set, S has 2|S| subsets.
M. If n and k are positive integers with , then C(n+1,k) = C(n, k) + C(n, k+1).
N. If n is a positive integer, then the alternating sums of all the C(n, k) are 0.
O. A finite set with n members has C(n, k) subsets of size k.