JEE Main Mathematics MCQs - Power Set, Relations, and Equivalence Relations

31.

Which of the following is the power set of the set A = {1, 2}?

a) {{1}, {2}, {1, 2}}
b) {{1, 2}, {}}
c) {{1, 2}, {1}, {2}, {}}
d) {{1}, {2}, {}, {1, 2}}

Answer: c) {{1, 2}, {1}, {2}, {}}

32.

The number of elements in the power set of a set with 4 elements is:

a) 8
b) 16
c) 4
d) 2

Answer: b) 16

33.

If A = {a, b, c}, what is the power set of A?

a) {a, b, c, {a, b, c}}
b) { {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
c) {a, b, c, {a}}
d) {a, b, c, {b, c}}

Answer: b) { {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}

34.

What is the relation between two sets A and B, if for every element x in A, x is also in B?

a) Universal relation
b) Identity relation
c) Subset relation
d) Empty relation

Answer: c) Subset relation

35.

Which of the following is true about a reflexive relation on set A?

a) For all elements a, b ∈ A, if aRb then bRa.
b) For all elements a ∈ A, aRa holds true.
c) For all elements a, b ∈ A, aRb implies a ≠ b.
d) For all elements a, b ∈ A, aRb implies a ≠ b.

Answer: b) For all elements a ∈ A, aRa holds true.

36.

Which of the following relations on the set of integers is reflexive?

a) x ≤ y
b) x = y
c) x > y
d) x < y

Answer: b) x = y

37.

In an equivalence relation, which of the following properties must hold?

a) Reflexive, symmetric, and transitive
b) Reflexive and transitive
c) Symmetric and transitive
d) Reflexive only

Answer: a) Reflexive, symmetric, and transitive

38.

Which of the following is a symmetric relation?

a) x ≤ y
b) x = y
c) x > y
d) x < y

Answer: b) x = y

39.

If a relation R on a set A is both reflexive and transitive, then which of the following is true?

a) It is an equivalence relation
b) It is symmetric
c) It is asymmetric
d) It is an anti-symmetric relation

Answer: a) It is an equivalence relation

40.

Which of the following is not a property of an equivalence relation?

a) Reflexivity
b) Symmetry
c) Transitivity
d) Anti-symmetry

Answer: d) Anti-symmetry

41.

If A = {1, 2, 3} and R is the relation on A such that R = {(1, 1), (2, 2), (3, 3)}, then the relation R is:

a) Reflexive only
b) Reflexive and symmetric
c) Reflexive, symmetric, and transitive
d) Transitive only

Answer: c) Reflexive, symmetric, and transitive

42.

Which of the following sets represents the relation R = {(1, 1), (2, 2), (3, 3)} on A?

a) Reflexive relation
b) Symmetric relation
c) Transitive relation
d) All of the above

Answer: d) All of the above

43.

The relation R on set A is called an equivalence relation if it satisfies:

a) Reflexive, symmetric, and transitive
b) Reflexive only
c) Symmetric and transitive only
d) Reflexive and anti-symmetric

Answer: a) Reflexive, symmetric, and transitive

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JEE Main Mathematics MCQs - Power Set, Relations, and Equivalence Relations

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