Discrete Mathematics Answers

1.b is defined by bn = n(−1)n, n ≥ 1

(a) Find Σ when 4 is on top, i=1 at the bottom and b_i at the right hand side

(b) Is b increasing, decreasing, non-increasing or non-decreasing?

4. v defined by vn = n! + 2, n ≥ 1.

(a) Find v3

(b) Find  Σ 4 on top , i=1 at the bottom and V_i on the right hand side of Sigma

(c) Is v increasing, decreasing, non-increasing or non-decreasing?

(a)   If x is nonnegative, then x is positive or x is 0. 

Create a schematic diagram of all odd numbers from 20 to 45

If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area.

Which of the following functions are injective? Which are surjective?

a) f: Z → Z given by f(x) = x² + 1.

b) g: N → N given by g(x) = 2^x.

c) h: R → R given by h(x) = 5x - 1.

Let f be the function from x ={0, 1, 2, 3, 4, 5} to X defined by

f(x) = 4x mod 6.

Write f as a set of ordered pairs and draw the arrow diagram of f . Is f one-to-one? Is f onto?

show that C(n+1,k)=C(n,k-1)+C(n,k)

Let R = {(1,4), (2,1), (2,5),(2,4),(4,3),(5,3),(3,2)} on the set A = {1, 2, 3, 4, 5}. Use Warshall’s algorithm to find transitive closure of R.