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If A = {a} and B = {b} are singleton sets, under what condition are A and B equal?

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Free Superintendent Of Survey And Land Records Practice Questions

Kerala Public Service CommissionRecruitment for Superintendent of Survey and Land Records in Kerala Government Service. The role involves managing survey and land records with a pay scale of ₹50,200 – 1,05,300.Direct recruitment2 vacancies available

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Q1. If A = {a} and B = {b} are singleton sets, under what condition are A and B equal?

  1. When a = b
  2. When a ≠ b
  3. When both sets have the same number of elements
  4. When either a or b is an element of the other set

Q2. Compare the union operation with the intersection operation on sets. Which of the following statements is true?

  1. Union results in a set with fewer elements than intersection
  2. Intersection always contains all elements of the union
  3. Union combines all elements from both sets without duplication
  4. Union and intersection always produce the same set

Q3. Which of the following best defines a finite set in elementary set theory?

  1. A set with no elements.
  2. A set with a countable number of elements.
  3. A set with a limited number of elements.
  4. A set with an infinite number of elements.

Q4. Consider the set S = {1, 2, 3, ..., 100}. Which of the following statements is true about S?

  1. Set S is infinite because it contains many elements.
  2. Set S is finite and has 100 elements.
  3. Set S is infinite because it contains natural numbers.
  4. Set S is finite but has an unknown number of elements.

Q5. Consider the universal set \( U = \{1, 2, 3, 4, 5\} \) and the empty set \( \emptyset \). What is the intersection of \( U \) and \( \emptyset \)?

  1. \( \{1, 2, 3, 4, 5\} \)
  2. \( \emptyset \)
  3. \( \{0\} \)
  4. Undefined

Q6. Given the set of all integers Z and the set of even integers E, which of the following best describes their cardinalities?

  1. Both Z and E are finite sets.
  2. Z is infinite, but E is finite.
  3. Both Z and E are infinite and have the same cardinality.
  4. E is infinite and has greater cardinality than Z.

Q7. Which of the following statements correctly defines the empty set?

  1. A set containing all possible elements.
  2. A set that contains no elements.
  3. A set that contains exactly one element.
  4. A set that contains only universal elements.

Q8. Which of the following statements correctly defines when two sets A and B are considered equal?

  1. A and B have the same number of elements.
  2. Every element of A is in B and every element of B is in A.
  3. A is a subset of B.
  4. A and B have no elements in common.

Q9. Given the sets B = {1, 2, 3} and C = {3, 4, 5}, which of the following correctly describes the union of B and C?

  1. {1, 2, 3, 4, 5}
  2. {3}
  3. {1, 2, 4, 5}
  4. {}

Q10. Compare the properties of the empty set and the universal set. Which of the following statements is false?

  1. The empty set is a subset of every set, including the universal set.
  2. The universal set is a subset of every set.
  3. The intersection of the universal set with any set \( A \) is \( A \).
  4. The union of the empty set with any set \( A \) is \( A \).

Q11. Which of the following sets is an example of an infinite set?

  1. The set of all natural numbers
  2. The set of months in a year
  3. The set of vowels in the English alphabet
  4. The set of days in a week

Q12. Given sets A = {1, 3, 5} and B = {2, 3, 4}, what is the union A ∪ B?

  1. {1, 2, 3, 4, 5}
  2. {3}
  3. {1, 3, 5}
  4. {2, 4}

Q13. Consider the set A = {2, 4, 6, 8}. Which type of set does A represent?

  1. Infinite set
  2. Empty set
  3. Finite set
  4. Universal set

Q14. Which statement correctly compares subset and proper subset?

  1. Every subset is a proper subset.
  2. A proper subset can be equal to the original set.
  3. A proper subset contains fewer elements than the original set.
  4. Subset and proper subset mean the same.

Q15. Given the universal set \( U = \{a, b, c, d\} \) and a set \( B = \{b, d\} \), what is the complement of the empty set \( \emptyset \) with respect to \( U \)?

  1. \( \emptyset \)
  2. \( U \)
  3. \{a, b, c, d, e\} \)
  4. \{b, d\} \)