Sets (Intermediate) Welcome to your Sets (Intermediate) 1. Let A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}. A. A ∪ B = {1, 2, 3, 4, 5} B. A ∩ B = {3, 4, 5} C. A ∪ B = {1, 2, 3, 4, 5, 6, 7} D. A ∩ B = {6, 7} None 2. Universe U = {1, …, 8}, A = {2, 4, 6, 8}, B = {1, 2, 3, 4}. Find (A ∪ B)′ (complement in U). A. {5, 6, 7, 8} B. {5, 7} C. {5, 6, 7} D. {6, 7, 8} None 3. Given |A| = 12, |B| = 9, |A ∩ B| = 4. Compute |A ∪ B|. A. 21 B. 17 C. 13 D. 5 None 4. If A ⊆ B, |B| = 15, |A| = 6, then |B \ A| = ? A. 9 B. 6 C. 21 D. 15 None 5. Let A = { x | x divides 24 exactly }. How many elements does A have? A. 6 B. 8 C. 12 D. 9 None 6. Given A = {1, 2, …, 10}, B = {2, 4, 6, 8, 10}, C = {1, 3, 5, 7, 9}. Find (B ∩ C)′, where complement is taken in A. A. ∅ B. A C. B D. C None 7. If A and B are disjoint sets with |A| = 7 and |A ∪ B| = 20, find |B|. A. 13 B. 14 C. 7 D. 27 None 8. Which identity is always true? A. A ∪ A′ = U B. A ∩ A′ = U C. A ∪ A = ∅ D. A ∩ A = ∅ None 9. De Morgan’s Law states: (A ∪ B)′ = ? A. A′ ∪ B′ B. A′ ∩ B′ C. A ∪ B D. A ∩ B None 10. In a class of 100 students, 70 passed Maths (M), 60 passed Physics (P), 50 passed Chemistry (C); 40 passed M∧P, 30 passed P∧C, 20 passed C∧M, and 10 passed all three. How many passed at least one subject? A. 150 B. 100 C. 90 D. 80 None 11. Let A = { multiples of 3 ≤ 30 }, B = { multiples of 5 ≤ 30 }. Then |A ∩ B| = ? A. 2 B. 3 C. 4 D. 5 None 12. Which of the following is De Morgan’s Law? A. (A ∩ B)′ = A′ ∩ B′ B. (A ∪ B)′ = A ∪ B C. (A ∩ B)′ = A′ ∪ B′ D. (A ∪ B)′ = A′ ∪ B′ None 13. If |A| = 3, then the power set 𝒫(A) has how many elements? A. 6 B. 8 C. 7 D. 9 None 14. Given A ⊆ B, which of the following holds? A. A ∪ B = A B. A ∩ B = A C. B \ A = B D. A ∩ B = B None 15. If A = {1, 2, 3, 4, 5}, B = {x | x > 3}, find A ∩ B. A. {1, 2, 3} B. {4, 5} C. {x > 3} D. {3, 4, 5} None 16. Define A Δ B = (A \ B) ∪ (B \ A). If U = {1…12}, A = {3,6,9,12}, B = {2,4,6,8,10,12}, then |A Δ B| = ? A. 6 B. 8 C. 4 D. 10 None 17. When does A ∪ B = A ∩ B? A. Always B. If A = B C. If A ∩ B = ∅ D. Never None 18. Which statement is always true for any sets A, B? A. A ⊆ A ∪ B B. B ⊆ A ∩ B C. A ∩ B ⊆ A ∪ B D. Both A and B None 19. In an exam of 60 students, 40 pass English, 35 pass Hindi, and 20 pass both. How many fail both? A. 15 B. 20 C. 5 D. 0 None 20. If A = { x ∈ ℤ | x² < 25 }, find |A|. A. 8 B. 9 C. 10 D. 11 None