Discrete Mathematics Answers

15. I provide 5 chairs, one for each person that is going to wait in the line. In how many different ways can they stand in line? 

Using a Truth table, determine the value of the compound proposition ((𝑝 ∨ 𝑞) ∧ (￢𝑝 ∨ 𝑟)) → (𝑞 ∨ 𝑟).

Let ‘R’ be a relation defined on a set of integers Z as follows:

∀ 𝑎, 𝑏 ∈ 𝑍, 𝑎𝑅𝑏 iff 𝑏 = a^r

for some integer 𝑟. Show that R is a partially

ordered relation.

Determine Which of these function are bijection from the set of real number to itself

1- f(x)=-3x+4

2- f(x)=-3x2+7

3- f(x)=(x+1)/(x+2)

In exercises 7-8, let X = {1 , 2} and Y = {a, b, c}. List the elements in each set.

X x Y

Let f : R → R be defined by f(x) = (x3 + 1)/2

a. Prove that f is bijective

b. Determine f -1 (x) and f o f o f -1

a) How many bytes are required to represent the decimal number -6357 in the EBCDIC packed decimal format?

Let f : R → R be defined by f(x) = 3√(1 – x 3 ). a. Prove that f is bijective b. Determine f -1 (x)

Find the sum-of-products expansions of these boolean functions: F(x,y,z) = x.

1. Given A = {2, 4, 6, 8} and B = {3, 4, 5, 6}, determine:

a. A U B

b. A ∩ B

2. Given A = {3, 5, 7, 9} and B = {4, 5, 6, 7}, determine:

a. A - B

b. B - A

c. A ∩ B