Discrete Mathematics Answers

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

1. Express the following statements using quantifiers.

A. All cats have fleas.

B. No one in this class knows how to speak Mandarin.

2.Form the negation of each statement without applying negation to the left of any quantifier.

3. Express each negation in simple English.

Part 2

1. Given A = {4, 8, 12, 16} and B = {6, 12, 18, 24}, determine the following:

a. A U B

b. A ∩ B

c. A - B

d. B - A

Use resolution to show the hypotheses “Allen is a bad

boy or Hillary is a good girl” and “Allen is a good boy or

David is happy” imply the conclusion “Hillary is a good

girl or David is happy.”