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

The statement asks whether \( D' \subset E \), where:

- \( U = \{p, q, r, s, t\} \)
- \( D = \{p, q, r, s\} \)
- \( E = \{s, t\} \)

### Step 1: Find \( D' \)
\( D' \) represents the complement of set \( D \) relative to the universal set \( U \). The complement of \( D \) is the set of elements in \( U \) that are not in \( D \).

Since \( D = \{p, q, r, s\} \), the complement \( D' \) would be:

\[
D' = U - D = \{p, q, r, s, t\} - \{p, q, r, s\} = \{t\}
\]

### Step 2: Check whether \( D' \subset E \)
We need to determine if the set \( D' = \{t\} \) is a subset of the set \( E = \{s, t\} \).

- A set \( A \) is a subset of another set \( B \) if every element of \( A \) is also an element of \( B \).

Since \( D' = \{t\} \) and \( t \) is in \( E = \{s, t\} \), it follows that \( D' \subset E \).

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

Would you like any further details or have any questions? Here are 5 related questions to consider:

1. What is the definition of set complement?
2. How would you determine if one set is a proper subset of another?
3. Can a set be a subset of itself?
4. How does the universal set affect the complement of a set?
5. What is the difference between a subset and a proper subset?

**Tip:** When working with set complements, always subtract the set from the universal set to ensure accuracy.

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

This page provides a solution to the set theory problem where U = {p, q, r, s, t}, D = {p, q, r, s}, E = {s, t}, and asks whether D' ⊂ E is true. The solution includes steps for finding the set complement and verifying the subset relation. Suitable for students in Grades 10-12.

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