Let's analyze the sets and the given statements to determine which are true.

The universal set $\xi$ is defined as the set of all integers: $\xi = \{ \text{all integers} \}$

Set $D$ is defined as: $D = \{ x : 5 < x \leq 12 \}$ This means $D$ includes all integers greater than 5 and less than or equal to 12. So, $D$ can be written as: $D = \{6, 7, 8, 9, 10, 11, 12\}$

Now, let's evaluate each statement:

1. $9.5 \in D$:

   • 9.5 is not an integer and $D$ contains only integers, so this statement is false.

2. $D = \emptyset$:

   • $D$ is not an empty set; it contains integers from 6 to 12. Hence, this statement is false.

3. $6 \in D$:

   • 6 is within the range $5 < 6 \leq 12$. Hence, this statement is true.

4. $3 \in D$:

   • 3 is not within the range $5 < 3 \leq 12$. Hence, this statement is false.

5. $12 \in D$:

   • 12 is within the range $5 < 12 \leq 12$. Hence, this statement is true.

6. $5 \in D$:

   • 5 is not within the range $5 < 5 \leq 12$. Hence, this statement is false.

The true statements are:

• $6 \in D$
• $12 \in D$

Would you like more details or have any questions about this solution? Here are some related questions:

1. How would the set $D$ change if the condition was $5 \leq x \leq 12$?
2. What is the cardinality of set $D$ as defined in the problem?
3. Can you list all the elements of the set $D$ explicitly?
4. What would the set $D$ be if the upper bound was changed to $x < 12$?
5. How would the interpretation change if $D$ included non-integer values within the same range?

Tip: When analyzing set membership, always ensure to check both the type of elements (e.g., integers, reals) and the range conditions (e.g., strict vs. inclusive inequalities).