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Let's go through the questions step by step. I'll start by solving Question 4 and move to the rest of the questions after.

### 4. If \( A = \{1, 2, 3, 4\}, B = \{2, 4, 6, 8\}, C = \{a, b, c, d\}, D = \{1, 2, a, c, e\} \), find:
- (a) \( A \cup B \): Union of sets A and B
- (b) \( A \cap B \): Intersection of sets A and B
- (c) \( C \cup B \): Union of sets C and B
- (d) \( C \cap D \): Intersection of sets C and D
- (e) \( A \cap D \): Intersection of sets A and D

**Solutions**:

- (a) \( A \cup B = \{1, 2, 3, 4, 6, 8\} \) (all unique elements from both sets).
- (b) \( A \cap B = \{2, 4\} \) (common elements between A and B).
- (c) \( C \cup B = \{a, b, c, d, 2, 4, 6, 8\} \) (all unique elements from C and B).
- (d) \( C \cap D = \{a, c\} \) (common elements between C and D).
- (e) \( A \cap D = \{1, 2\} \) (common elements between A and D).

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Would you like to continue with the Venn diagram problems or explore a different section? Here's a list of 5 possible next steps:

1. Move on to question 5 and analyze the Venn diagram.
2. Further explain the intersection and union concepts in more detail.
3. Explore how to represent these sets visually with a Venn diagram.
4. Review the concept of set cardinality.
5. Dive deeper into the properties of set operations, such as commutativity.

**Tip:** In set theory, the union \( A \cup B \) always includes every element from both sets, while the intersection \( A \cap B \) only includes the elements common to both.

Solve set theory and Venn diagram problems involving union, intersection, and cardinality of sets.

This page explores set theory concepts, including union, intersection, and cardinality, with detailed solutions to problems involving Venn diagrams. Suitable for Grades 6-9.

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