# Susanne Epp, Discrete Math An introduction to mathematical reasonin...

## Question

Susanne Epp, Discrete Math An introduction to mathematical reasoning, brief edition..
section 6.3

find a counterexample..
(2) for all sets A and B, (A UNION B)ᶜ = Aᶜ UNION Bᶜ

prove if it is true, or find a counterexample if it is false
(7) For all sets A, B, C, (A-B) INTERSECT (C-B) = A - (B UNION C).

construct an algebraic proof for the given statement. cite a property from theorem 6.2.2 for every step
(34) For all sets A, B, C, (A-B) - C = A- (B UNION C)

(37) For all sets A and B, (Bᶜ UNION (bᶜ - A ))ᶜ = B

Simplify the given expression, cite a property from theorem 6.2.2 for each step.

(41) A INTERSECT ((B UNION Aᶜ) INTERSECT Bᶜ)

Section 1.3
(12) Define a relation T from R to R as follows: For all real numbers x and y, (x, y) in T means that y² - x² = 1. Is T a function? Explain.

(20)

Define functions H and K from R to R by the following formulas: For all x in R, H(x) = (x-2)² and K(x) = (x-1)(x-3)+1. Does H=K? Explain.

Section 7.1

(16) Let F and G be functions from the set of all real numbers to itself. Define new functions F-G: R->R and G-F: R->R as follows: For all x in R,

(F-G)(x) = F(x) - G(x)
(G-F)(x) = G(x) - F(x)

Does F-G = G-F? Explain.

(28)
Student C tries to define a function h: Q-> Q by the rule h(m/n) = (m²)/n for all integers m and n with n != 0. Student D claims that h is not well defined. Justify student D's claim.

(32)
Let X= {1,2,3,4} and Y= {a,b,c,d,e}. Define g: X->Y as follows: g(1) = a, g(2) = a, g(3) = a, and g(4) = d.

(a) draw an arrow diagram for g.
(b) Let A = {2,3}, C={a}, and D={b,c}. Find g(A), g(X), g⁻¹(C), g⁻¹(D), and g⁻¹(Y)

let X and Y be sets, let A and B be any subsets of X, and let C and D be any subsets of Y. Determine which of the properties are true for all function F from X to Y and which are false for at least one function F from X to Y. Justify answers.

(37)
For all subsets A and B of X, F(A-B) = F(A) - F(B).

## Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

By purchasing this solution you'll be able to access the following files:
Solution.pdf.

\$15.00
for this solution

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Discrete Math Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.

We couldn't find that subject.
Please select the best match from the list below.

We'll send you an email right away. If it's not in your inbox, check your spam folder.

• 1
• 2
• 3
Live Chats