Let U = {p, q, r, s, t},  D =
{q, s, p, r},
E =
{r, t},
F = {p, t}, and G = {s}. Determine whether the statement is true or false.
D' ⊂ E

To determine whether the statement \( D' \subset E \) is true or false, let's break it down step by step.

### Definitions and Steps:
1. **Universal Set (U):**  
   \( U = \{p, q, r, s, t\} \)

2. **Set \( D \):**  
   \( D = \{q, s, p, r\} \)

3. **Complement of Set \( D \) (denoted as \( D' \)):**  
   The complement of \( D \) in \( U \) is the set of elements in \( U \) that are not in \( D \).
   \[
   D' = U \setminus D = \{t\}
   \]

4. **Set \( E \):**  
   \( E = \{r, t\} \)

5. **Subset Relation:**  
   Now, we check if \( D' \subset E \).  
   \( D' = \{t\} \) and \( E = \{r, t\} \).

   Since all elements of \( D' \) (which is just \( \{t\} \)) are in \( E \), we conclude that \( D' \subset E \).

### Conclusion:
The statement \( D' \subset E \) is **true**.

Would you like more details or have any questions?

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Here are 5 related questions to consider:
1. How do you find the complement of a set in a universal set?
2. What are the differences between proper subsets and regular subsets?
3. Can a set be a subset of itself?
4. How do you determine if a statement involving sets is true or false?
5. How would the result change if \( U \) were a different universal set?

**Tip:** A subset \( A \) of a set \( B \) means every element of \( A \) is also in \( B \).

Let U = {p, q, r, s, t}, D = {q, s, p, r}, E = {r, t}, F = {p, t}, and G = {s}. Determine whether the statement is true or false: D' ⊂ E.

Learn how to determine if D' is a subset of E given the universal set U = {p, q, r, s, t} and sets D, E, F, and G. This problem explores key concepts in set theory, including subsets and complements. Suitable for students in Grades 9-12.

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