Test 

1. The closure property of addition in ℝ implies that:
A. a − b ∈ ℝ
B. a + b ∈ ℝ
C. ab ∈ ℝ
D. a/b ∈ ℝ

2. Which property guarantees that ab = ba?
A. Associative
B. Distributive
C. Commutative
D. Closure

3. The identity element for addition satisfies:
A. a + 1 = a
B. a + 0 = a
C. a × 0 = a
D. a − 1 = a

4. If a + b = 0, then b equals:
A. a
B. −a
C. 1/a
D. 0

5. The multiplicative inverse of a (a ≠ 0) satisfies:
A. a + a⁻¹ = 1
B. a × a⁻¹ = 1
C. a − a⁻¹ = 0
D. a² = 1

6. Which of the following demonstrates distributive property?
A. ab = ba
B. (ab)c = a(bc)
C. a(b + c) = ab + ac
D. a + b = b + a

7. If ab = 0 and a ≠ 0, then:
A. a = 0
B. b = 0
C. ab = 1
D. b ≠ 0

8. Which statement is equivalent to a/b = c/d?
A. a + d = b + c
B. ad = bc
C. a − d = b − c
D. ab = cd

9. The expression (ab)⁻¹ equals:
A. ab
B. a⁻¹ + b⁻¹
C. a⁻¹ b⁻¹
D. a/b

10. The uniqueness of identity means:
A. There are many identities
B. Only one identity element exists
C. Identity does not exist
D. Identity depends on a

Answer Key (Test)

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