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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 \( U \)?

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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. 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\} \)

Q2. 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

Q3. 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.

Q4. 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

Q5. Given two sets P = {1, 2, 3} and Q = {3, 2, 1}, which of the following is true?

  1. P and Q are equal sets.
  2. P is a subset of Q but not equal.
  3. Q is a subset of P but not equal.
  4. P and Q are disjoint sets.

Q6. In a survey, 40 people like tea, 30 people like coffee, and 15 people like both tea and coffee. How many people like tea or coffee?

  1. 55
  2. 70
  3. 85
  4. 25

Q7. Which of the following sets is an example of a singleton set?

  1. {0}
  2. {1, 2}
  3. {}
  4. {a, b, c}

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. 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

Q10. 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

Q11. 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.

Q12. 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.

Q13. If a set A is infinite and a set B is finite, which of the following statements is always true?

  1. The union of A and B is finite.
  2. The union of A and B is infinite.
  3. The intersection of A and B is infinite.
  4. The difference B \ A is infinite.

Q14. 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}

Q15. 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
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