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

Q2. 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

Q3. Calculate the number of singleton subsets of the set M = {a, b, c, d}.

  1. 1
  2. 2
  3. 4
  4. 16

Q4. 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.

Q5. 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 \( A \).

Q6. 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

Q7. 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.

Q8. 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

Q9. Consider the set S = {x | x is a natural number less than 5}. Which of the following is a singleton set related to S?

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

Q10. Which of the following sets is an example of a singleton set?

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

Q11. 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.

Q12. In a survey, the universal set \( U \) represents all land parcels in a district. If \( A \) is the set of parcels surveyed this year and \( \emptyset \) is the empty set, which of the following statements is always true?

  1. \( A \cup \emptyset = \emptyset \)
  2. \( A \cap \emptyset = A \)
  3. \( A \cup \emptyset = A \)
  4. \( A \cap U = \emptyset \)

Q13. 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.

Q14. 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

Q15. 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.
Free Superintendent Of Survey And Land Records Practice Questions | Kerala PSC Prep