daily practice problem on set theory

QUESTION PAPER ON SETS


MULTIPLE CHOICE QUESTIONS (1–12)
1. If A = {x : x = n2 − 1, n ∈ N, n ≤ 5}, then the number of elements in A is:
(A) 4 (B) 5 (C) 6 (D) 7

2. The set builder form of {3, 6, 9, 12, 15, 18} is:
(A) {x : x = 3n, n ∈ (B) {x : x = 3n, n ∈
N, 1 ≤ n ≤ 6} W, 1 ≤ n ≤ 6}
(C) {x : x = 3n, n ∈ (D) {x : x = 3n, n ∈
N, n ≤ 6} W, n ≤ 6}

3. If A = {1, 2, 3}, B = {2, 3, 4}, and C = {3, 4, 5}, then (A ∩ B) ∪ C equals:
(A) {1, 3, 4, 5} (B) {2, 3, 4, 5} (C) {3, 4, 5} (D) {1, 2, 3, 4, 5}

4. The number of proper subsets of a set containing n elements is:
(A) 2n (B) 2n − 1 (C) 2n − 2 (D) 2n−1

5. If n(A) = 5, n(B) = 7, and n(A ∪ B) = 10, then n(A ∩ B) equals:
(A) 2 (B) 3 (C) 4 (D) 5

6. Which of the following is an empty set?
(A) {x : x2 = 4, x ∈ (B) {x : x2 = 9, x ∈
N} Z}
(C) {x : x2 = −1, x ∈ (D) {x : x2 = 16, x ∈
R} Z}

7. If A and B are disjoint with n(A) = 4, n(B) = 5, then n(A ∪ B) =
(A) 9 (B) 1 (C) 20 (D) 0

8. Number of subsets of a 4-element set that contain a particular element:
(A) 4 (B) 8 (C) 16 (D) 32

9. The set of all subsets of a set is called:
(A) Universal set (B) Power set (C) Super set (D) Proper set

10. If A ∪ B = A ∩ B, then:
(A) A = ∅ (B) B = ∅ (C) A = B (D) A ⊂ B

11. If n(A) = 20, n(B) = 30, n(A ∩ B) = 10, then n(A△B) =
(A) 20 (B) 30 (C) 40 (D) 50

12. {x : x is prime and x < 10} in roster form:
(A) {2, 3, 5, 7} (B) {1, 2, 3, 5, 7} (C) {2, 3, 5, 7, 9} (D) {2, 3, 5, 7, 11}

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