JEE Main - Union intersection and complement of sets Online Test (MCQ Quiz)

1. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is the union of A and B (A ∪ B)?

A) {1, 2, 3, 4, 5, 6} B) {3, 4} C) {1, 2, 5, 6} D) {1, 2, 3, 4}

2. Given A = {a, b, c} and B = {c, d, e}, what is the intersection of A and B (A ∩ B)?

A) {a, b, c, d, e} B) {c} C) {a, b, d, e} D) {a, b}

3. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the universal set and A = {2, 4, 6, 8}. What is the complement of A (A')?

A) {1, 3, 5, 7, 9} B) {2, 4, 6, 8} C) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} D) {}

4. Which property states that for any two sets A and B, A ∪ B = B ∪ A?

A) Associative Property B) Distributive Property C) Commutative Property of Union D) Idempotent Property

5. The intersection of two sets A and B, denoted by A ∩ B, contains elements that are:

A) In set A only B) In set B only C) In both set A and set B D) In either set A or set B or both

6. If A ⊆ B, then A ∪ B is equal to:

A) A B) B C) ∅ (empty set) D) U (universal set)

7. If A ∩ B = ∅, then sets A and B are called:

A) Equal sets B) Disjoint sets C) Subset D) Superset

8. What is (A ∪ B)'?

A) A' ∪ B' B) A' ∩ B' C) A ∩ B D) A ∪ B

9. What is (A ∩ B)'?

A) A' ∪ B' B) A' ∩ B' C) A ∪ B D) A ∩ B

10. Which of the following is NOT a property of set union?

A) A ∪ ∅ = A B) A ∪ A = A C) A ∪ U = U D) A ∪ B = A ∩ B

11. Which of the following is NOT a property of set intersection?

A) A ∩ ∅ = ∅ B) A ∩ A = A C) A ∩ U = A D) A ∩ B = A ∪ B

12. For any set A, A ∪ A' is equal to:

A) A B) A' C) U (universal set) D) ∅ (empty set)

13. For any set A, A ∩ A' is equal to:

A) A B) A' C) U (universal set) D) ∅ (empty set)

14. If A = {1, 3, 5} and B = {2, 4, 6}, what is A ∪ B?

A) {1, 2, 3, 4, 5, 6} B) {1, 3, 5} C) {2, 4, 6} D) ∅

15. If A = {apple, banana, cherry} and B = {banana, date, fig}, what is A ∩ B?

A) {apple, banana, cherry, date, fig} B) {apple, cherry} C) {banana} D) {date, fig}

16. Let U = {all integers} and A = {even integers}. What is A'?

A) {even integers} B) {odd integers} C) {prime integers} D) {composite integers}

17. The distributive property of intersection over union states that:

A) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) B) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) C) A ∪ B = B ∪ A D) A ∩ B = B ∩ A

18. The distributive property of union over intersection states that:

A) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) B) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) C) A ∪ B = B ∪ A D) A ∩ B = B ∩ A

19. If A = {x | x is a natural number less than 5} and B = {x | x is a natural number greater than 3 and less than 7}, what is A ∪ B?

A) {1, 2, 3, 4, 5, 6} B) {4, 5, 6} C) {1, 2, 3} D) {1, 2, 3, 4, 5, 6, 7}

20. Using the sets from the previous question, what is A ∩ B?

A) {4} B) {1, 2, 3} C) {5, 6} D) {1, 2, 3, 4, 5, 6}

21. Let U = {1, 2, 3, 4, 5} and A = {1, 2}. What is the number of elements in A'?

A) 2 B) 3 C) 5 D) 0

22. If |A| = 5, |B| = 7, and |A ∩ B| = 3, what is |A ∪ B|?

A) 15 B) 9 C) 12 D) 8

23. If |A ∪ B| = 10, |A| = 6, and |B| = 7, what is |A ∩ B|?

A) 1 B) 3 C) 13 D) 16

24. The complement of the complement of a set A is:

A) ∅ B) U C) A' D) A

25. If A and B are any two sets, which of the following is always true?

A) A ∪ B = A ∩ B B) A ∩ B ⊆ A ∪ B C) A ∪ B ⊆ A ∩ B D) A ∩ B = ∅

26. Let A = {1, 2, 3} and B = {3, 4, 5}. What is the set difference A - B?

A) {1, 2} B) {3} C) {4, 5} D) {1, 2, 3, 4, 5}

27. Let A = {1, 2, 3} and B = {3, 4, 5}. What is the set difference B - A?

A) {1, 2} B) {3} C) {4, 5} D) {1, 2, 3, 4, 5}

28. The symmetric difference of two sets A and B, denoted by A Δ B, is defined as:

A) (A ∪ B) - (A ∩ B) B) A ∩ B C) A ∪ B D) A' ∪ B'

29. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is A Δ B?

A) {3, 4} B) {1, 2, 5, 6} C) {1, 2, 3, 4, 5, 6} D) {1, 5, 6}

30. Which property relates union and intersection in the form A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)?

A) Commutative Property B) Associative Property C) Distributive Property D) Idempotent Property

31. Which property relates intersection and union in the form A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)?

A) Commutative Property B) Associative Property C) Distributive Property D) Identity Property

32. If A = {prime numbers less than 10} and B = {odd numbers less than 10}, what is A ∩ B?

A) {2, 3, 5, 7} B) {1, 3, 5, 7, 9} C) {3, 5, 7} D) {2, 3, 5, 7, 9}

33. Using the sets from the previous question, what is A ∪ B?

A) {2, 3, 5, 7} B) {1, 3, 5, 7, 9} C) {2, 3, 5, 7, 1, 9} D) {1, 2, 3, 5, 7, 9}

34. Let U = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5}. What is the number of elements in A ∪ A'?

A) 3 B) 6 C) 0 D) 9

35. If A ∩ B = A, this implies:

A) A ⊆ B B) B ⊆ A C) A = B D) A and B are disjoint

36. If A ∪ B = B, this implies:

A) A ⊆ B B) B ⊆ A C) A = B D) A and B are disjoint

37. What is the relationship between A - B and B - A?

A) A - B = B - A B) (A - B) ∪ (B - A) = A Δ B C) (A - B) ∩ (B - A) = A ∪ B D) (A - B) ∩ (B - A) = A ∩ B

38. The formula for the number of elements in the union of two sets is given by:

A) |A ∪ B| = |A| + |B| B) |A ∪ B| = |A| + |B| - |A ∩ B| C) |A ∪ B| = |A| + |B| + |A ∩ B| D) |A ∪ B| = |A| - |B|

39. If A = {vowels in the English alphabet} and B = {letters in the word 'EDUCATION'}, what is A ∩ B?

A) {E, U, A, I, O} B) {E, D, U, C, A, T, I, O, N} C) {E, U, A, I, O} D) {E, D, C, T, N}

40. Using the sets from the previous question, what is A ∪ B?

A) {E, U, A, I, O} B) {E, D, U, C, A, T, I, O, N} C) {E, D, U, C, A, T, I, O, N} D) {E, U, A, I, O, D, C, T, N}

41. If A and B are two sets such that A ∩ B = A, then which of the following is true?

A) B ⊆ A B) A ⊆ B C) A = B D) A ∪ B = ∅

42. If U is the universal set and A is any set, then A ∪ U is:

A) A B) U C) ∅ D) A'

43. If U is the universal set and A is any set, then A ∩ U is:

A) A B) U C) ∅ D) A'

44. Which law states that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)?

A) De Morgan's Law B) Distributive Law C) Associative Law D) Commutative Law

45. Which law states that (A ∪ B)' = A' ∩ B'?

A) Distributive Law B) Commutative Law C) Associative Law D) De Morgan's Law

46. Which law states that (A ∩ B)' = A' ∪ B'?

A) De Morgan's Law B) Distributive Law C) Associative Law D) Commutative Law

47. If A = {1, 2, 3} and B = {1, 2, 3}, what is A ∪ B?

A) {1, 2, 3} B) {1, 2} C) {3} D) ∅

48. If A = {1, 2, 3} and B = {1, 2, 3}, what is A ∩ B?

A) {1, 2, 3} B) {1, 2} C) {3} D) ∅

49. Let U = {a, b, c, d, e} and A = {a, c}. What is A' ∩ A?

A) {b, d, e} B) {a, c} C) ∅ D) U

50. If A ⊆ B, then A ∩ B is equal to:

A) A B) B C) ∅ D) U

Union intersection and complement of sets - Online Test

Test Results