Check all the statements that are true If n is a nonnegative

Check all the statements that are true: If n is a nonnegative integer, then the sum of all the C(n, k) is 2^n. An injective function from a set of n elements to a set of n elements is automatically surjective. 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. The cardinality of a Cartesian product of sets is the product of the cardinalities of the individual sets. If n and k are positive integers with n greaterthanorequalto k, then C(n + 1, k) = C(n, k) + C(n, k + 1). If n is a nonnegative integer, then the alternating sums of all the C(n, k) are 0. If n and r are nonnegative integers and r lessthanorequalto n, then C(n, r) = P(n, r)/r!. 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. If S is a finite set, S has 2|S| subsets. A finite set with n members has C(n, k) subsets of size k. Combinations C(n, r) are symmetrical in r with respect to the point r = n/2. There are n^m functions from a set of n elements to a set of m elements. A surjective function from a set of n elements to a set of n elements is automatically injective. If there are 2n+1 objects in n boxes, then at least one box must contain at least 3 objects. There is no! bijections from a set with n elements to itself.

Solution

A) false

B( true

C) true

D) true

E) true

F) false

G) true

H) true

I) false it has 2^|S| elements

J) true

K) true

L) false

M) true

N) true

O) true