Exam (elaborations)
Discrete Mathematics With Application 4th Edition by Susanna S. Epp - Test Bank
- Module
- Mathematics
- Institution
- Mathematics
Complete Test Bank (with Questions Answers)
[Show more]
Content preview
,Discrete Mathematics with Applications, 4th Editionby Susanna S. Epp
Test Bank Questions: Updated March 2013
Chapter 1
1. Fill in the blanks to rewrite the following statement with variables: Is there an integer with a
remainder of 1 when it is divided by 4 and a remainder of 3 when it is divided by 7?
(a) Is there an integer n such that n has ?
(b) Does there exist such that if n is divided by 4 the remainder is 1 and if ?
2. Fill in the blanks to rewrite the following statement with variables:
Given any positive real number, there is a positive real number that is smaller.
(a) Given any positive real number r, there is s such that s is .
(b) For any , such that s < r.
3. Rewrite the following statement less formally, without using variables:
There is an integer n such that 1/n is also an integer.
4. Fill in the blanks to rewrite the following statement:
For all objects T , if T is a triangle then T has three sides.
(a) All triangles .
(b) Every triangle .
(c) If an object is a triangle, then it .
(d) If T , then T .
(e) For all triangles T , .
5. Fill in the blanks to rewrite the following statement:
Every real number has an additive inverse.
(a) All real numbers .
(b) For any real number x, there is for x.
(c) For all real numbers x, there is real number y such that .
6. Fill in the blanks to rewrite the following statement:
There is a positive integer that is less than or equal to every positive integer.
(a) There is a positive integer m such that m is .
(b) There is a such that every positive integer.
(c) There is a positive integer m which satisfies the property that given any positive integer
n, m is .
7. (a) Write in words how to read the following out loud {n ∈ Z | n is a factor of 9}.
(b) Use the set-roster notation to indicate the elements in the set.
, 8. (a) Is {5} ∈ {1, 3, 5}?
(b) Is {5} ⊆ {1, 3, 5}?
(c) Is {5} ∈ {{1}, {3}, {5}}?
(d) Is {5} ⊆ {{1}, {3}, {5}}?
9. Let A = {a, b, c} and B = {u, v}. Write a. A × B and b. B × A.
10. Let A = {3, 5, 7} and B = {15, 16, 17, 18}, and define a relation R from A to B as follows: For
all (x, y) ∈ A × B,
y
(x, y) ∈ R ⇔ is an integer.
x
(a) Is 3 R 15? Is 3 R 16? Is (7, 17) ∈ R? Is (3, 18) ∈ R?
(b) Write R as a set of ordered pairs.
(c) Write the domain and co-domain of R.
(d) Draw an arrow diagram for R.
(e) Is R a function from A to B? Explain.
11. Define a relation R from R to R as follows: For all (x, y) ∈ R × R, (x, y) ∈ R if, and only if,
x = y 2 + 1.
(a) Is (2, 5) ∈ R? Is (5, 2) ∈ R? Is (−3) R 10? Is 10 R (−3)?
(b) Draw the graph of R in the Cartesian plane.
(c) Is R a function from R to R? Explain.
12. Let A = {1, 2, 3, 4} and B = {a, b, c}. Define a function G: A → B as follows:
G = {(1, b), (2, c), (3, b), (4, c)}.
(a) Find G(2).
(b) Draw an arrow diagram for G.
13. Define functions F and G from R to R by the following formulas:
F (x) = (x + 1)(x − 3) and G(x) = (x − 2)2 − 7.
Does F = G? Explain.
Chapter 2
1. Which of the following is a negation for “Jim is inside and Jan is at the pool.”
(a) Jim is inside or Jan is not at the pool.
(b) Jim is inside or Jan is at the pool.
(c) Jim is not inside or Jan is at the pool.
(d) Jim is not inside and Jan is not at the pool.
(e) Jim is not inside or Jan is not at the pool.
2
, 2. Which of the following is a negation for “Jim has grown or Joan has shrunk.”
(a) Jim has grown or Joan has shrunk.
(b) Jim has grown or Joan has not shrunk.
(c) Jim has not grown or Joan has not shrunk.
(d) Jim has grown and Joan has shrunk.
(e) Jim has not grown and Joan has not shrunk.
(f) Jim has grown and Joan has not shrunk.
3. Write a negation for each of the following statements:
(a) The variable S is undeclared and the data are out of order.
(b) The variable S is undeclared or the data are out of order.
(c) If Al was with Bob on the first, then Al is innocent.
(d) −5 ≤ x < 2 (where x is a particular real number)
4. Are the following statement forms logically equivalent: p ∨ q → p and p ∨ (∼ p ∧ q)? Include a
truth table and a few words explaining how the truth table supports your answer.
5. State precisely (but concisely) what it means for two statement forms to be logically equivalent.
6. Write the following two statements in symbolic form and determine whether they are logically
equivalent. Include a truth table and a few words explaining how the truth table supports
your answer.
If Sam bought it at Crown Books, then Sam didn’t pay full price.
Sam bought it at Crown Books or Sam paid full price.
7. Write the following two statements in symbolic form and determine whether they are logically
equivalent. Include a truth table and a few words explaining how the truth table supports
your answer.
If Sam is out of Schlitz, then Sam is out of beer.
Sam is not out of beer or Sam is not out of Schlitz.
8. Write the converse, inverse, and contrapositive of “If Ann is Jan’s mother, then Jose is Jan’s
cousin.”
9. Write the converse, inverse, and contrapositive of “If Ed is Sue’s father, then Liu is Sue’s
cousin.”
10. Write the converse, inverse, and contrapositive of “If Al is Tom’s cousin, then Jim is Tom’s
grandfather.”
11. Rewrite the following statement in if-then form without using the word “necessary”: Getting
an answer of 10 for problem 16 is a necessary condition for solving problem 16 correctly.
12. State precisely (but concisely) what it means for a form of argument to be valid.
3
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller premiumbiz379. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £19.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
64438 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy revision notes and other study material for 14 years now