**Critical Read and Review Description. Thoroughly discuss and answer all Questions and follow steps 1-5. **

**Step 1.**

### 1. Make sure to review the textbook readings and module notes before beginning this homework. **1-2 Textbook Reading and Module Notes**

*Discrete Mathematical Structures*

Section 1.1

Section 1.2

Section 1.3 (through example 14)

Section 1.5 (through example 7)

- For additional practice, each homework problem has some ungraded examples and sample problems from the text that you can review, and they directly correspond with your graded homework.
- Work on those problems if needed,
- Work within this document for your homework, and be sure to show all steps for arriving at your solution in

Section 1.1 (1-3)

Section 1.2 (1-2)

Section 1.3 (1-4)

Section 1.5 (1-3)

- Use attached formula sheet as needed to help with your equations.
- You can use it anytime throughout the course to help with the equation tool.
7. Please refer to the Problem Set Rubric document in the Assignment Guidelines and Rubrics section of the course.

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**Step 2. **

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**Section 1.1 Homework **

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1) Suppose C = {red, blue, gray, orange}. For a) and b) below, fill in the value(s) that makes the statement true (Note: More than one answer is possible). This problem is similar to example 1 and problems 1.1.1 and 1.1.2.

- a) _____
- b) _____

2) List the elements of the set . This problem is similar to examples 2 and 5 and problem 1.1.4.

3) Consider U = {2, ♣, ♫, ®}, A={a, ♫, ®}, and B={2, ♫}. Complete parts a) and b) below. This problem is similar to examples 3, 7, and 8 and problems 1.1.15 and 1.1.16.

- a) Is ? Explain why.

- b) Is ? Explain why.

**Step 3.**

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**Section 1.2 Homework **

1) Consider the following sets:

U = {pink, purple, red, blue, gray, orange, green, yellow, indigo, violet}

A = {orange, purple, red, yellow}

B = {blue, gray, orange}

C = {pink, violet, red}

Compute each of the following:

- a) =
- b) =
- c) =
- d) =
- e) =

This problem is similar to examples 1, 2, 4, and 6 and problems 1.2.1–1.2.4.

2) The records of 200 SNHU students show the following courses taken:

104 students took Latin

103 students took Greek

35 students took Sanskrit

46 students took Latin and Greek

24 students took Greek and Sanskrit

9 students took all 3

28 students took none of these languages

How many students took *only *Greek?

How many students took Latin and Sanskrit, but not Greek?

Review Theorem 3. This problem is similar to example 10 and problems 1.2.25–1.2.28.

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**Step 4.**

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**Section 1.3 Homework**

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1) Give the set corresponding to the sequence: yabbadabbadoo. This problem is similar to examples 3, 9, and 11 and problems 1.3.1–1.3.4.

2) Consider the sequence defined by .

Is this a recursive or explicit equation? Explain why.

Using the formula, list the first 4 terms of the sequence (starting with n=1).

This problem is similar to examples 4–7 and problems 1.3.7–1.3.14.

3) Consider the sequence defined by a_{1} = 2 and a_{n }= 2 – a_{n-1}. _{ }

_{ }

Is this a recursive or explicit equation? Explain why.

Using the formula, list the first 4 terms of the sequence (starting with n=1).

This problem is similar to examples 4–7 and problems 1.3.7–1.3.14.

4) Consider the following sets:

U = {pink, purple, red, blue, gray, orange, green, yellow, indigo, violet}

A = {orange, purple, red, yellow}

B = {blue, gray, orange}

C = {pink, violet, red}

Represent each of the following with an array of zeros and ones:

- a) =

- b) =

- c) =

This problem is similar to examples 12 and 13 and problems 1.3.26 and 1.3.27.

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**Step5.**

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**Section 1.5 Homework**

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Answer problems 1–3 using the following matrices:

A = B =

1) Identify the following values:

a_{13 }= , a_{21 }= , b_{12 }= , b_{21 }=

This problem is similar to example 1 and problem 1.5.1 parts a, b, and c.

2) Compute A + A.

This problem is similar to example 5 and problem 1.5.5 part a.

3) Of A•B and B•A, only one product is defined.

Explain which product is **undefined** and why.

Evaluate the product that is defined.

This problem is similar to example 7 and problem 1.5.5 part b.

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