Set Theory Objective Type Questions and Answers

(21) R is a relation on N given by N = {(x, y): 4x + 3y = 20}. Which of the following belongs to R?

[A] (– 4, 12)

[B] (5, 0)

[C] (3, 4)

[D] (2, 4)

Answer: (2, 4)

(22) Let X be a family of sets and R be a relation in X, defined by ‘A is disjoint from B’. Then, R is

[A] reflexive

[B] symmetric

[C] anti-symmetric

[D] transitive

Answer: symmetric

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(23) If A = { (1, 2, 3}, then the relation R = {(2, 3)} in A is

[A] Symmetric And Transitive Only

[B] Symmetric Only

[C] Transitive Only

[D] Not Transitive

Answer: Not Transitive

(24) The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y) : | x2 – y2| < 16} is given by

[A] {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)}

[B] {(2, 2), (3, 2), (4, 2), (2, 4)}

[C] {(3, 3), (4, 3), (5, 4), (3, 4)}

[D] None of the above

Answer: A = {1, 2, 3} and B = {2, 1, 3}

(25) The set O of odd positive integers less than 10 can be expressed by _____________

[A] {1, 2, 3}

[B] {1, 3, 5, 7, 9}

[C] {1, 2, 5, 9}

[D] {1, 5, 7, 9, 11}

Answer: {1, 3, 5, 7, 9}

(26) What is the cardinality of the set of odd positive integers less than 10?

[A] 10

[B] 5

[C] 3

[D] 20

Answer: 5

(27) The set of positive integers is _____________

[A] Infinite

[B] Finite

[C] Subset

[D] Empty

Answer: Infinite

(28) What is the Cardinality of the Power set of the set {0, 1, 2}.

[A] 8

[B] 6

[C] 7

[D] 9

Answer: 8

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