Quiz 

1. The real number system is defined as a set equipped with which of the following?
A. One operation only
B. Two operations and an order relation
C. Three operations
D. Only ordering

2. Which set includes negative numbers and zero?
A. ℕ
B. ℤ
C. ℚ
D. ℝ

3. Rational numbers are of the form:
A. m + n
B. m/n where n ≠ 0
C. √m
D. m²

4. Which axiom ensures a(b + c) = ab + ac?
A. Commutative
B. Associative
C. Distributive
D. Closure

5. The trichotomy law states that:
A. a + b = b + a
B. Exactly one of a < b, a = b, a > b holds
C. a(b + c) = ab + ac
D. a² ≥ 0

6. The completeness property is related to:
A. Addition
B. Multiplication
C. Ordering
D. Supremum

7. Which set is NOT complete?
A. ℝ
B. ℚ
C. Both
D. None

8. The multiplicative identity in ℝ is:
A. 0
B. −1
C. 1
D. 2

9. If a < b, then a + c < b + c illustrates:
A. Closure
B. Compatibility
C. Identity
D. Inverse

10. Irrational numbers are introduced to:
A. Simplify integers
B. Fill gaps in ℚ
C. Remove fractions
D. Replace ℤ

Answer Key (Quiz)

1-B, 2-B, 3-B, 4-C, 5-B, 6-D, 7-B, 8-C, 9-B, 10-B