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Free download in PDF Set Theory Multiple Choice Questions and Answers for competitive exams. These short objective type questions with answers are very important for competitive exams as well as Board exams. These short solved questions or quizzes are provided by Gkseries.
(1)
A __________ is an ordered collection of objects.
[A]
Relation
[B]
Function
[C]
Set
[D]
Proposition
(2)
Power set of empty set has exactly _________ subset.
[A]
One
[B]
Two
[C]
Zero
[D]
Three
(3)
What is the Cartesian product of A = {1, 2} and B = {a, b}?
[A]
{(1, a), (1, b), (2, a), (b, b)}
[B]
{(1, 1), (2, 2), (a, a), (b, b)}
[C]
{(1, a), (2, a), (1, b), (2, b)}
[D]
{(1, 1), (a, a), (2, a), (1, b)}
Answer: {(1, a), (2, a), (1, b), (2, b)}
(4)
Which of the following two sets are equal?
[A]
A = {1, 2} and B = {1}
[B]
A = {1, 2} and B = {1, 2, 3}
[C]
A = {1, 2, 3} and B = {2, 1, 3}
[D]
A = {1, 2, 4} and B = {1, 2, 3}
Answer: A = {1, 2, 3} and B = {2, 1, 3}
(5)
The members of the set S = {x | x is the square of an integer and x < 100} is ________________
[A]
{0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
[B]
{0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
[C]
{1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
[D]
{0, 1, 4, 9, 16, 25, 36, 49, 64, 121}
Answer: {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
(6)
The number of subsets of a set containing n elements is
[A]
n
[B]
2n 1
[C]
n2
[D]
2n
(7)
If A = {1, 3, 5, B} and B = {2, 4} then
[A]
4 A
[B]
{4} A
[C]
B A
[D]
180° and 0°
(8)
The symmetric difference of A = {1, 2, 3} and B = {3, 4, 5} is
[A]
{1, 2}
[B]
{1, 2, 4, 5}
[C]
{4, 3}
[D]
{2, 5, 1, 4, 3}
(9)
If A = {1, 2} and B = {0, 1}, then A B is
[A]
{(1, 0) (1, 1), (2, 0) (2, 1)}
[B]
{(1, 0), (2, 1)}
[C]
{(1, 1), (1, 2), (0, 1) (0, 2)
[D]
None of these
Answer: {(1, 0) (1, 1), (2, 0) (2, 1)}
(10)
If A = {1, 2, 3}, B = {3, 4, 5}, then (A B) A is
[A]
{(1, 3), (2, 3), (3, 3)}
[B]
{(3, 1), (3, 2), (3, 3)
[C]
{(1, 3), (3, 1), (3, 2)
[D]
None of these
Answer: {(3, 1), (3, 2), (3, 3)
(11)
If A = {2, 3, 4}, B = {2, 5, 6}, then (A B) (A B) is
[A]
{(3, 2), (3, 3), (3, 5)
[B]
{(3, 2), (3, 5) (3, 6)
[C]
{(3, 2), (3, 5)}
[D]
None of these
(12)
If A = {1, 2}, B = {2, 3} and C = {4}, then A B C is
[A]
{(1, 2, 4), (2, 2, 4), (1, 3, 4), (2, 3, 4)
[B]
{(1, 2, 4), (1, 4, 3), (2, 3, 4)
[C]
{(1, 3, 4), (2, 3, 4), (2, 1, 3), (2, 2, 4)
[D]
None of these
Answer: {(1, 2, 4), (2, 2, 4), (1, 3, 4), (2, 3, 4)
(13)
If A = {2, 3} and B = {x | x N and x < 3}, then A B is
[A]
{(2, 1), (2, 2), (3, 1), (3, 2)}
[B]
{(1, 2), (1, 3), (2, 2), (2, 3)}
[C]
{(1, 2), (2, 2), (3, 3), (3, 2)
[D]
None of these
Answer: {(2, 1), (2, 2), (3, 1), (3, 2)}
(14)
If R = {x, y) : x, y Z, x2 + y2 4} is a relation in z, then domain of R is
[A]
{0, 1, 2}
[B]
{– 2, – 1, 0}
[C]
{– 2, – 1, 0, 1, 2}
[D]
None of these
Answer: {– 2, – 1, 0, 1, 2}
(15)
R is a relation defined in Z by aRb if and only if ab 0, then R is
[A]
reflexive
[B]
symmetric
[C]
transitive
[D]
equivalence
(16)
If R be relation ‘<‘ from A = {1, 2, 3, 4} to B = {1, 3, 5} ie, (a, b) R iff a < b, then RoR– 1 is
[A]
{(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}
[B]
{(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}
[C]
{(3, 3), (3, 5), (5, 3), (5, 5)}
[D]
{ (3, 3), (3, 4), (4, 5)}
Answer: {(3, 3), (3, 5), (5, 3), (5, 5)}
(17)
R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R – 1 is
[A]
{(11, 8), (13, 10)}
[B]
{(8, 11), (10, 13)}
[C]
{(8, 11), (9, 12), (10, 13)}
[D]
None of the above
Answer: {(8, 11), (10, 13)}
(18)
Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then, n (X Y) is equal to
(19)
Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is
[A]
7
[B]
9
[C]
10
[D]
12
(20)
The relation R defined on the set of natural numbers as {(a, b): a differs from b by 3} is given
[A]
{(1, 4), (2, 5), (3, 6), ….}
[B]
{ (4, 1), (5, 2), (6, 3), ….}
[C]
{(4, 1), (5, 2), (6, 3), ….}
[D]
None of the above
Answer: { (4, 1), (5, 2), (6, 3), ….}
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