The task involves describing each set in words and then representing it using the Roster Method. Here’s how each set can be interpreted and represented:

a) $P = \{ x \mid x^2 = 9 \}$

• Word description: The set $P$ contains elements $x$ where $x^2 = 9$.
• Solution: $x^2 = 9$ implies $x = \pm 3$ (i.e., $x = 3$ or $x = -3$).
• Roster Method: $P = \{-3, 3\}$

b) $Q = \{ x \mid x - 10 = 0 \}$

• Word description: The set $Q$ contains elements $x$ where $x - 10 = 0$, which implies $x = 10$.
• Roster Method: $Q = \{10\}$

c) $R = \{ x \mid x \text{ is a positive number and a negative number} \}$

• Word description: The set $R$ includes both positive and negative numbers, which would theoretically be all integers except zero.
• Roster Method: $R = \{\ldots, -2, -1, 1, 2, \ldots\}$

d) $S = \{ x \mid x \text{ is a letter in the word "PURWOKERTO KOTA SATRIA"} \}$

• Word description: The set $S$ consists of the distinct letters that form the phrase "PURWOKERTO KOTA SATRIA".
• Roster Method: $S = \{P, U, R, W, O, K, E, T, A, S, I\}$

e) $T = \{ x \mid 0 < x < 11, x \text{ is an integer} \}$

• Word description: The set $T$ includes integers $x$ that are greater than 0 and less than 11.
• Roster Method: $T = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$

Would you like more details on any specific part of this explanation?

Five related questions:

1. What is the difference between the Roster Method and the Set-Builder Notation?
2. How can we generalize the set $P = \{ x \mid x^2 = 9 \}$ for any equation $x^2 = a$?
3. What would the set $Q$ look like if the equation was $x + 5 = 0$?
4. Can a set have both positive and negative numbers in real-world scenarios? How would you describe such a set?
5. How do you remove duplicates when creating a set from a phrase, as in set $S$?

Tip:

When using the Roster Method, ensure that all elements in the set are unique and well-defined.