Here is the analysis for each question:

Question 1

Given: A is a set of prime numbers less than 15. The correct enumeration of set A is:

• a. $A = \{1, 3, 5, 7, 11, 13\}$
• b. $A = \{2, 3, 5, 7, 11, 13\}$
• c. $A = \{1, 3, 5, 7, 11\}$
• d. $A = \{2, 3, 5, 7, 9, 11, 13\}$

Explanation: The prime numbers less than 15 are $\{2, 3, 5, 7, 11, 13\}$. Hence, the correct answer is:

• b. $A = \{2, 3, 5, 7, 11, 13\}$.

Question 2

Given: The following is a set of an infinite set:

• a. $P = \{ \text{Bilangan bulat kurang dari 10} \}$
• b. $Q = \{ \text{Bilangan asli antara 5 dan 27} \}$
• c. $R = \{ \text{Bilangan cacah antara 10 dan 25} \}$
• d. $S = \{ \text{Bilangan prima antara 30 dan 40} \}$

Explanation: An infinite set in this context is the one that keeps growing. Among the options, $P$ represents all integers less than 10, and it is limited. The other sets are finite or limited, while:

• b. and c. are finite.
• d. is finite. Hence, the correct answer is:
• a. $P = \{ \text{Bilangan bulat kurang dari 10} \}$.

Question 3

Given: $P = \{1, 2, 3, 4, 5\}$ and $Q = \{2, 3, 4, 5, 6, 7, 8\}$. The relation $R$ from set $P$ to set $Q$ includes:

• a. $R = \{(1, 2), (2, 3), (3, 4), (5, 6)\}$

Explanation: The correct relation is based on the function's definition. So, you check for possible combinations.

• R includes pairs where each element from set $P$ maps to one from set $Q$. This is a given set of ordered pairs:
• Correct answer: a. $R = \{(1, 2), (2, 3), (3, 4), (5, 6)\}$.

Question 4

Given: $A = \{3, 5\}$ and $B = \{1, 2, 3, 4, 5, 6, 7, 8\}$. The relation from set $A$ to set $B$ is “greater than.”

• a. $\{3, 5\}$
• b. $\{1, 2, 3, 4\}$
• c. $\{4, 5, 6, 7, 8\}$
• d. $\{1, 2, 3, 4, 5, 6, 7, 8\}$

Explanation: The relation "greater than" will refer to elements in $B$ greater than those in $A$. From this, you can determine the resulting range.

• Correct answer: c. $\{4, 5, 6, 7, 8\}$.

Question 5

Given: $A = \{1, 2, 3, 4, 5\}$ and $B = \{a, b, c, d\}$. The number of possible mappings (functions) from set $A$ to set $B$ is:

• a. 20
• b. 64
• c. 625
• d. 1,024

Explanation: The number of functions from set $A$ to set $B$ is given by $|B|^{|A|}$, which is the number of choices for each element in $A$. Here $|A| = 5$ and $|B| = 4$, so the number of functions is $4^5 = 1024$.

• Correct answer: d. 1,024.

Would you like more details on any of these solutions or have further questions? Here's some follow-up questions:

1. Can you explain why the set of prime numbers less than 15 excludes 1?
2. How can we determine whether a set is infinite or finite?
3. How do you define the "greater than" relation between two sets?
4. Can you explain the concept of "functions" between sets in more detail?
5. How does the formula $|B|^{|A|}$ relate to calculating functions from one set to another?

Tip: Always verify the set elements carefully to ensure that you're not including numbers that do not belong to the category you're focusing on, like including 1 as a prime number.