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.