Here is the solution to the questions in the image:

1. Use set notation to describe the following sets:

a. $A = \{ 2, 4, 6, 8, 10 \}$: The set can be described as: $A = \{ x \mid x = 2n, n \in \mathbb{N}, 1 \leq n \leq 5 \}$ This describes $A$ as the set of even numbers starting from $2$ up to $10$.

b. $B = \{ 1, 4, 9, 16, \dots \}$: The set can be described as: $B = \{ x \mid x = n^2, n \in \mathbb{N} \}$ This represents $B$ as the set of perfect squares of natural numbers.

c. $C = \{ 15, 13, 19, 11, 17 \}$: The set can be described as: $C = \{ x \mid x \text{ is a prime number between 10 and 20 } \}$

2. If $a = 3$ and $b = 5$, write the values of:

a. $|a + b|$: $|a + b| = |3 + 5| = |8| = 8$

b. $|a - b|$: $|a - b| = |3 - 5| = |-2| = 2$

c. $|a| - |b|$: $|a| - |b| = |3| - |5| = 3 - 5 = -2$

Do you have any specific questions or need further clarification?

Related Questions:

1. How can we describe sets with infinite elements using set-builder notation?
2. What are the common properties of prime numbers in a given range?
3. Can you give examples of other types of sequences (e.g., geometric, arithmetic)?
4. Why is the absolute value operation always non-negative?
5. What is the difference between $|a - b|$ and $|b - a|$?

Tip:

When working with sets, always identify the pattern or rule that generates the elements of the set.