## Test Bank For Discrete Mathematics with Application 4th Edition

**ISBN-10: 8131533026, ISBN-13: 978-8131533024**

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,

(x, y) ∈ R ⇔

y

x

is an integer.

(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 A to B? 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.

## Reviews

There are no reviews yet.