How would the result change if we calculated the union of only two of the sets, say d and e

Let's calculate the union of only the sets \( D \) and \( E \) to see how the result changes.

Given:
- \( D = \{4, 7, 9\} \)
- \( E = \{4, 6, 7, 8\} \)

To find the union \( D \cup E \), we combine all the unique elements from both sets \( D \) and \( E \).

1. Start with the elements in \( D \): \( \{4, 7, 9\} \).
2. Add the elements from \( E \) that are not already in \( D \): \( \{4, 6, 7, 8\} \) (add 6 and 8).

So, the union of \( D \) and \( E \) is:

\[
D \cup E = \{4, 6, 7, 8, 9\}
\]

### Comparison with the Union of All Three Sets:
- The union of \( D \), \( E \), and \( F \) was \(\{3, 4, 5, 6, 7, 8, 9\}\).
- The union of just \( D \) and \( E \) is \(\{4, 6, 7, 8, 9\}\).

**Difference:** The set \( D \cup E \) lacks the elements 3 and 5, which were contributed by set \( F \) in the complete union of \( D \cup E \cup F \).

Would you like further clarification or to explore more related questions? Here are five questions that might interest you:

1. What would the union of sets \( D \) and \( F \) look like?
2. How can you verify the union of sets using Venn diagrams?
3. What happens if we take the union of the intersection of \( D \) and \( E \) with another set?
4. What is the difference between union and symmetric difference in set theory?
5. How can set union operations be applied in database queries?

**Tip:** When taking the union of sets, always include each unique element only once, even if it appears in more than one set.

Explore how to calculate the union of sets D and E, including step-by-step examples and explanations. Understand the concept of set union in set theory and its application to specific sets D and E. Suitable for Grades 7-9.

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