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**SY Ex (1)**

**Q1.** State the set of even numbers in roster form and set builder form.

- **Ans:** 
  - Roster form: \( \{2, 4, 6, 8, 10, \dots\} \)
  - Set builder form: \( \{x | x = 2n, n \in \mathbb{N}\} \)

**Q2.** State \( A \cap B \), \( A \cup B \), \( A - B \) if
- \( A = \{x : x \text{ is a prime number less than 10}\} \)
- \( B = \{x : x \text{ is an even number less than 10}\} \)

- **Ans:**
  - \( A \cap B = \{2\} \)
  - \( A \cup B = \{2, 3, 4, 5, 6, 7, 8\} \)
  - \( A - B = \{3, 5, 7\} \)

**Q3.** State the commutative property for addition and multiplication of sets.

- **Ans:**
  - \( A \cup B = B \cup A \)
  - \( A \cap B = B \cap A \)

**Q4.** If \( \{x : x \text{ is a prime number}\} = \{2, 3, 5, 7, 11, 13, \dots\} \), find equal sets.

**Q5.** State the idempotent property for union and intersection of sets.

- **Ans:**
  - \( A \cup A = A \)
  - \( A \cap A = A \)

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Explore set theory questions and answers including even numbers in roster and set builder form, union, intersection, and properties of sets. Learn about commutative and idempotent properties in set operations.

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