JEE Main - Algebraic properties of sets Online Test (MCQ Quiz)

1. Which property states that for any sets A, B, and C, the union of A with the union of B and C is the same as the union of the union of A and B with C?

A) Commutative Property of Union B) Associative Property of Union C) Distributive Property of Union over Intersection D) Identity Property of Union

2. The property A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) is known as:

A) Distributive Property of Union over Intersection B) Distributive Property of Intersection over Union C) Associative Property of Union D) Commutative Property of Intersection

3. What is the result of A ∩ (B ∪ C) according to the distributive property?

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

4. The property that states A ∪ B = B ∪ A for any sets A and B is called:

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

5. Which property demonstrates that A ∩ B = B ∩ A for any sets A and B?

A) Associative Property of Intersection B) Commutative Property of Intersection C) Idempotent Property of Intersection D) Symmetric Property of Intersection

6. The property A ∪ A = A is an example of:

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

7. What is the idempotent property for intersection of a set with itself?

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

8. If U is the universal set, then A ∪ U is equal to:

A) A B) U C) ∅ D) A ∩ U

9. For any set A and the universal set U, A ∩ U is equal to:

A) U B) A C) ∅ D) A ∪ U

10. What is the result of A ∪ ∅, where ∅ is the empty set?

A) ∅ B) A C) U D) A ∩ ∅

11. The intersection of any set A with the empty set ∅ is:

A) A B) ∅ C) U D) A ∪ ∅

12. Which property states that A ∪ (A ∩ B) = A?

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

13. The property A ∩ (A ∪ B) = A is known as:

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

14. Which property states that A ∪ B = B ∪ A and A ∩ B = B ∩ A?

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

15. The property (A ∪ B) ∪ C = A ∪ (B ∪ C) is called:

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

16. The property (A ∩ B) ∩ C = A ∩ (B ∩ C) is called:

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

17. Which property ensures that if we take the union of a set with itself, the result is the same set?

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

18. The property A ∩ A = A is an example of:

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

19. If A ⊆ B, what is A ∪ B equal to?

A) A B) B C) ∅ D) A ∩ B

20. If A ⊆ B, what is A ∩ B equal to?

A) A B) B C) ∅ D) A ∪ B

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

A) Commutative Property of Union B) Associative Property of Intersection C) Distributive Property of Union over Intersection D) Absorption Property

22. The property A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) is known as:

A) Distributive Property of Intersection over Union B) Distributive Property of Union over Intersection C) Commutative Property of Intersection D) Associative Property of Union

23. Which property is demonstrated by A ∪ ∅ = A?

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

24. The property A ∩ ∅ = ∅ is an example of:

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

25. Which property states that A ∪ U = U, where U is the universal set?

A) Identity Property B) Commutative Property C) Complement Property D) Absorption Property

26. The property A ∩ U = A, where U is the universal set, is an example of:

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

27. Which property ensures that the order of sets does not matter in union or intersection?

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

28. The property A ∪ (B ∪ C) = (A ∪ B) ∪ C applies to which operation?

A) Intersection only B) Union only C) Both Union and Intersection D) Neither Union nor Intersection

29. The property (A ∩ B) ∩ C = A ∩ (B ∩ C) applies to which operation?

A) Union only B) Intersection only C) Both Union and Intersection D) Neither Union nor Intersection

30. Which property can be stated in two forms: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) and A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)?

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

31. The property A ∪ (A ∩ B) = A is known as:

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

32. The property A ∩ (A ∪ B) = A is also known as:

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

33. Which property is related to the identity element for union being the empty set?

A) Commutative B) Associative C) Identity D) Idempotent

34. Which property is related to the identity element for intersection being the universal set?

A) Commutative B) Associative C) Identity D) Idempotent

35. The property that states A ∪ A = A is the property of:

A) Commutativity B) Associativity C) Idempotence D) Distributivity

36. The property A ∩ A = A is the property of:

A) Commutativity B) Associativity C) Idempotence D) Distributivity

37. Which property implies that A ∪ B = B ∪ A?

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

38. Which property implies that A ∩ B = B ∩ A?

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

39. The property (A ∪ B) ∪ C = A ∪ (B ∪ C) is an example of:

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

40. The property (A ∩ B) ∩ C = A ∩ (B ∩ C) is an example of:

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

41. Which property is demonstrated by A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)?

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

42. The property A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) is an example of:

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

43. Which property states that A ∪ ∅ = A and A ∩ U = A?

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

44. The property A ∪ A = A and A ∩ A = A are examples of:

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

45. If A ⊆ B, then A ∪ B = B and A ∩ B = A. These are consequences related to:

A) Commutative and Associative Properties B) Distributive and Absorption Properties C) Properties of subsets D) Identity and Idempotent Properties

46. Which property states that for any sets A and B, A ∪ (A ∩ B) = A?

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

47. The property A ∩ (A ∪ B) = A is also known as the:

A) Distributive Law B) Commutative Law C) Absorption Law D) Associative Law

48. Which property states that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)?

A) Commutative B) Associative C) Distributive D) Absorption

49. The property A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) is an application of the:

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

50. Which property is demonstrated by A ∪ ∅ = A?

A) Commutative B) Associative C) Identity D) Idempotent

Algebraic properties of sets - Online Test

Test Results