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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.

Find the result of A ∩ (B' ∪ C) ∪ D, where U = {t, a, d, p, o, l, e, s}, A = {p, o, l, e}, B = {a, d, o, p, t}, C = {t, a, p, s}, and D = {l, e, a, s, t}.

Explore how to solve a set theory problem involving union, intersection, and complement of sets with the universal set U = {t, a, d, p, o, l, e, s}. We calculate B' and find the result of A ∩ (B' ∪ C) ∪ D step by step.

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