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

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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. 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.

Q2. 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\} \)

Q3. Suppose a surveyor is counting the number of distinct land plots in a newly developed area. If the number of plots is finite, which of the following statements must be true?

  1. The set of land plots is infinite because land is continuous.
  2. The set of land plots has a finite cardinality equal to the number of plots counted.
  3. The set of land plots is infinite because each plot can be subdivided infinitely.
  4. The set of land plots is empty.

Q4. 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

Q5. 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

Q6. Which of the following sets is an example of a singleton set?

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

Q7. 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. {}

Q8. 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.

Q9. 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.

Q10. 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}

Q11. Consider two sets A and B where A ∪ B = A. Which of the following statements must be true?

  1. B is a subset of A
  2. A is a subset of B
  3. A and B are disjoint
  4. A and B have no elements in common

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. 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.

Q14. Which of the following best describes the union of two sets A and B?

  1. The set of elements common to both A and B
  2. The set of all elements that are in A, or in B, or in both
  3. The set of elements in A but not in B
  4. The set of elements in B but not in A

Q15. 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 \( A \).
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