# Category: Lessons

Theorem NT 5.1: Every natural number $n>1$ is either prime or divisible by a prime.

Theorem NT 5.2: Suppose $p$ is prime and $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ are $n$ integers, where $n \geq 2$. If $p \mid a_{1} \cdot a_{2} \cdot a_{3} \cdot \ldots \cdot a_{n},$ then $p \mid a_{i}$ for at least one of the $a_{i}(1 \leq i \leq n)$.

Theorem NT 5.3: If $n$ is an integer greater than 1 then $n$ can be written as a product of primes.
(HINT: Prove using strong induction. Consider two cases, when $k+1$ is prime, and when it is composite)

Hi everyone! This online lesson is provided as a resource – we will also go over this material in class. Lesson 8: Negating Statements, Counting Lists

Topic. This lesson covers:

1. Sec 2.10 Negating Statements
2. Sec 3.1 Counting Lists
3. Sec 3.2 Factorials

Learning Outcomes.

• Apply rules for negating various types of statements, both in formal logic and natural language
• Count collections of lists with various properties

Homework. There is one WeBWorK assignment on today’s material (Note: some of the material in this assignment will be covered in the next lesson):

1. WeBWorK: WeBWorK Assignment5-Sec3.1-3.4

Lecture Notes:

Hi everyone! This online lesson is provided as a resource – we will also go over this material in class.

Hi everyone! This online lesson is provided as a resource – we will also go over this material in class. Lesson 4: Indexed Sets

Topic. This lesson covers:

• Sec 1.8: Indexed Sets

Learning Outcomes.

• Take unions and intersections of collections of sets indexed by the natural numbers or other sets.

Homework. There is 1 written assignment on today’s material:

1. Homework: Section 1.8 p.29: 3, 5, 6, 8

Lecture Notes:

Hi everyone! This online lesson is provided as a resource – we will also go over this material in class. Lesson 2: Cartesian Products and Subsets

Topic. This lesson covers:

• Sec 1.2: Cartesian Products
• Sec 1.3: Subsets

Learning Outcomes.

• Identify and manipulate ordered pairs and Cartesian products of sets.
• Identify and manipulate subsets of sets.

WeBWorK. There is 1 WeBWorK assignment on today’s material:

1. Assignment1-Sec1.2-1.3

Lecture Notes: