Here are some set theory exercises for you to practice:

1. Basic Set Operations

Let $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$. Find:

• a) $A \cup B$
• b) $A \cap B$
• c) $A - B$
• d) $B - A$
• e) $A \Delta B$ (symmetric difference of $A$ and $B$)

2. Power Set

Given the set $C = \{a, b, c\}$, find the power set of $C$.

3. Set Membership and Subsets

Let $D = \{x \, | \, x \text{ is an even number less than 10}\}$ and $E = \{0, 2, 4, 6, 8\}$.

• a) Is $4 \in D$?
• b) Is $D \subseteq E$?
• c) Is $E \subseteq D$?
• d) Find $D \cup E$ and $D \cap E$.

4. Cartesian Product

Let $F = \{1, 2\}$ and $G = \{x, y\}$. Find the Cartesian product $F \times G$.

5. Venn Diagram

Draw a Venn diagram to illustrate the relationship between three sets: $H = \{1, 2, 3, 4\}$, $I = \{3, 4, 5, 6\}$, and $J = \{2, 3, 6, 7\}$. Indicate the regions corresponding to $(H \cup I) \cap J$.

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Tip:

Always check if sets are subsets or supersets of each other before performing operations. This helps simplify calculations.

Would you like to see detailed solutions for any of these problems or more exercises?

Here are 5 related questions for further exploration:

1. What is the difference between a subset and a proper subset?
2. How is the complement of a set defined in a universal set?
3. What is the significance of De Morgan’s laws in set theory?
4. How do you prove that the power set of a set with $n$ elements has $2^n$ elements?
5. Can a set be both finite and infinite? Why or why not?