Let U = {p, q, r, s, t},  D = {p, r, s, t},  E = {q, s},  F =
{r, s},
and G = {s}. Determine whether the statement is true or false.
F ⊂ D

The statement \( F \subset D \) means that set \( F \) is a **subset** of set \( D \). A set \( F \) is a subset of another set \( D \) if all elements of \( F \) are also elements of \( D \).

### Let's check this:

- Set \( F = \{r, s\} \)
- Set \( D = \{p, r, s, t\} \)

Now, look at the elements of \( F \):
- Element \( r \) is in \( D \).
- Element \( s \) is in \( D \).

Since all elements of \( F \) are in \( D \), we can conclude that:

\[
F \subset D
\]

### Therefore, the statement \( F \subset D \) is **true**.

Would you like any further details or have any questions?

Here are 5 related questions to explore:
1. What is the difference between a subset and a proper subset?
2. Can a set be a subset of itself?
3. What does \( F \subseteq D \) mean, and how is it different from \( F \subset D \)?
4. Is the empty set a subset of all sets?
5. If \( G = \{s\} \), is \( G \subset F \)?

**Tip**: A set is always a subset of itself, but it is only a **proper subset** if it doesn't contain all elements of the other set.

Let U = {p, q, r, s, t},  D = {p, r, s, t},  E = {q, s},  F = {r, s}, and G = {s}. Determine whether the statement is true or false. F ⊂ D

Explore the basics of set theory by determining whether set F is a subset of set D. This problem involves understanding the concept of subsets and verifying set relationships, suitable for students in Grades 6-8.

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