The image you uploaded appears to contain a problem related to set theory. Here is what I can extract from the image:

1. You are given four sets:

• Universal set $U = \{ t, a, d, p, o, l, e, s \}$
• Set $A = \{ p, o, l, e \}$
• Set $B = \{ a, d, o, p, t \}$
• Set $C = \{ t, a, p, s \}$
• Set $D = \{ l, e, a, s, t \}$

2. You are tasked to find: $A \cap (B' \cup C) \cup D$

To solve this, follow these steps:

Step 1: Find $B'$ (the complement of $B$)

The complement of $B$ with respect to the universal set $U$ is: $B' = U - B = \{ t, a, d, p, o, l, e, s \} - \{ a, d, o, p, t \} = \{ l, e, s \}$

Step 2: Calculate $B' \cup C$ (union of $B'$ and $C$)

Now, find the union of $B'$ and $C$: $B' \cup C = \{ l, e, s \} \cup \{ t, a, p, s \} = \{ l, e, s, t, a, p \}$

Step 3: Find $A \cap (B' \cup C)$ (intersection of $A$ and $B' \cup C$)

Next, calculate the intersection of set $A$ and $B' \cup C$: $A \cap (B' \cup C) = \{ p, o, l, e \} \cap \{ l, e, s, t, a, p \} = \{ p, l, e \}$

Step 4: Calculate the final union with $D$

Now, find the union of $A \cap (B' \cup C)$ and $D$: $\{ p, l, e \} \cup \{ l, e, a, s, t \} = \{ p, l, e, a, s, t \}$

Final Answer:

The result of $A \cap (B' \cup C) \cup D$ is: $\{ p, l, e, a, s, t \}$

Let me know if you need further details or have any questions.

Here are 5 related questions to explore:

1. What is the difference between union and intersection of sets?
2. How do we define the complement of a set?
3. Can a set's union ever be smaller than its intersection?
4. How would the problem change if the universal set $U$ were different?
5. How does set theory apply to probability and logic?

Tip: Always double-check the universal set when finding complements, as it directly affects the result.