TS 10th Class Maths Bits Chapter 2 Sets

Solving these TS 10th Class Maths Bits with Answers Chapter 2 Sets Bits for 10th Class will help students to build their problem-solving skills.

Sets Bits for 10th Class

Question 1.
The symbol for a null set is
A) ∈
B) ∪
C) ϕ
D) \(\not \subset\)
Answer:
C) ϕ

Question 2.
C = {x : x is a circle in a given plane} is
A) finite set
B) infinite set
C) universal set
D) void set
Answer:
B) infinite set

Question 3.
Which of the following set is infinite?
A) The set of natural numbers ≤ 100
B) The set of even natural numbers between 50 and 100.
C) The set of points on a circle.
D) The set of prime numbers between 10 and 50.
Answer:
C) The set of points on a circle.

Question 4.
The number of elements in the set D = {x : x is a day of the week} is
A) 6
B) 4
C) 5
D) 7
Answer:
D) 7

Question 5.
The symbol for “implies” is
A) ⇒
B) ⇔
C) ⊂
D) \(\supset\)
Answer:
A) ⇒

Question 6.
If A = {1, 2, 3} the number of subsets of A is
A) 3
B) 8
C) 9
D) 6
Answer:
B) 8

Question 7.
Two sets A and B are said to be disjoint if
A) A∪B = ϕ
B) A – B = ϕ
C) B – A = ϕ
D) A ∩ B = ϕ
Answer:
D) A ∩ B = ϕ

Question 8.
For every set A, A ∩ ϕ =
A) ϕ
B) A
C) 0
D) 1
Answer:
A) ϕ

Question 9.
For every set A, A ∩ A =
A) 1
B) 0
C) A
D) ϕ
Answer:
C) A

Question 10.
If A and B are two sets, then x ∈ A ∩ B ⇒
A) x ∈ A or x ∈ B
B) x ∈ A and x ∈ B
C) x ∈ A and x \(\notin\) B
D) x\(\notin\)A and x ∈ B
Answer:
B) x ∈ A and x ∈ B

Question 11.
If A and B are two sets, then x ∈ A∪B ⇒
A) x ∈A and x\(\notin\)B
B) x\(\notin\)A and x∈B
C) x ∈ A or x ∈ B
D) x\(\notin\)A and x\(\notin\)B
Answer:
C) x ∈ A or x ∈ B

Question 12.
If A and B are two sets, then x ∈ A – B ⇒
A) x ∈ A or x ∈ B
B) x ∈ A and x ∈ B
C) x\(\notin\)A and x∈B
D) x\(\notin\)A and x\(\notin\)B
Answer:
D) x\(\notin\)A and x\(\notin\)B

Question 13.
If V = {a, e, i, o, u} and B = {a, i, k, u} then V – B =
A) {a, e, i, o, u}
B) {a, e, o, u}
C) {e, o}
D) {a, e, o}
Answer:
C) {e, o}

Question 14.
The shaded portion in the adjacent figure represents

A) A ∩ B
B) A ∪ B
C) A – B
D) A ⊂ B
Answer:
B) A ∪ B

Question 15.
The shaded portion in the adjacent figure represents

A) A ∩ B
B) A ∪ B
C) A ⊂ B
D) B ⊂ A
Answer:
A) A ∩ B

Question 16.
The shaded portion in the adjacent figure represents
A) A ⊂ B
(B) B ⊂ A
(C) B – A
(D) A – B
Answer:
(C) B – A

Question 17.
Which of the following sets are equal ?
A) E = {1, 0}, H = {a, b)
B) A = {0, a}, C = {b, 0}
C) D = {4, 8, 12}, F = {8, 12, 4}
D) G = {1, 5, 7, 11}, I = {1, 2, 3, 4}
Answer:
C) D = {4, 8, 12}, F = {8, 12, 4}

Question 18.
If A = {1, 3} and B = {1, 5, 9} then A – B =
A) {3}
B) {1}
C) {5, 9}
D) {1, 3, 5, 9}
Answer:
A) {3}

Question 19.
Which of the following sets in infinite ?
A) {x : x ∈ N and (x – 1 )(x – 2) = 0}
B) {x : x ∈ N and x² = 9}
C) {x : x ∈ N and 2x – 1 = 0}
D) {x : x ∈ N and x is odd}
Answer:
D) {x : x ∈ N and x is odd}

Question 20.
Which of the following sets finite ?
A) {x : x ∈ N and x is prime}
B) {x : x ∈ N and x is an even number less than 20}
C) {x : x² = 4 and x is an odd integer}
D) {x : x² is an even prime greater than 2}
Answer:
B) {x : x ∈ N and x is an even number less than 20}

Question 21.
Set of human being that reside on moon is ………
A) finite set
B) null set
C) infinite set
D) universal set
Answer:
B) null set

Question 22.
Which of the following is true in the following venn diagram ……..

A) A ∪B = ϕ
B) A ∪ B = µ
C) A ∩ B = µ
D) A ∩ B = ϕ
Answer:
D) A ∩ B = ϕ

Question 23.
Which of the following is an example for finite set
A) {x / x ∈ N and x² = 9}
B) Set of rational numbers in between 2 and 3
C) Multiples of even primes
D) Set of all primes
Answer:
A) {x / x ∈ N and x² = 9}

Question 24.
The number of subsets of the null set ϕ is ……….
A) 0
B) 1
C) 3
D) 4
Answer:
B) 1

Question 25.
If A = (a, b, c, d), how many subsets does the set ‘A’ have
A) 5
B) 6
C) 16
D) 65
Answer:
C) 16

Question 26.
A = {1, 2, 3, 7, 8}; B = {4, 5, 6, 7} find A ∩ B
A) {1, 2, 3, 4, 5, 6, 7, 8}
B) 7
C) ϕ
D) {7, 8}
Answer:
B) 7

Question 27.
n(A) = 14; n (B) = 11; n(A ∩ B) = 19 then n(A ∪B) = ……
A) 6
B) 16
C) 22
D) 25
Answer:
A) 6

Question 28.
The shaded area in the figure shows.

A) A – B
B) B – A
C) A ∆ B
D) (A ∪ B) (A ∩ B)
Answer:
C) A ∆ B

Question 29.
If ‘A’ and ‘B’ are two sets such that A ⊂ B then A ∪ B =
A) A
B) B
C) A ∩ B
D) None
Answer:
B) B

Question 30.
If ‘A’ and ‘B’ are disjoint sets then n(A ∩ B) = …….
A) 1
B) ϕ
C) 0
D) { }
Answer:
D) { }

Question 31.
Match the following :
Group -1 Group – II

Answer:
A) L → (iii), M → (i), N → (ii), O → (iv)
B) L → (i), M → (ii), N → (iii), O → (iv)
C) L → (iii), M → (i), N → (iv), O → (ii)
D) L → (iii), M → (ii), N → (ii), O → (iv)
Answer:
A) L → (iii), M → (i), N → (ii), O → (iv)

Question 32.
A ∩ ϕ = ………
A) A
B) ϕ
C) ϕ – A
D) { }
Answer:
A) A

Question 33.
Let A = {1, 2, {1}, {1, 2}, 3, 4}, then which of the following is true ?
A) {3} ∈ A
B) {1, 3} ∈ A
C) {1, 2} ∈ A
D) None
Answer:
C) {1, 2} ∈ A

Question 34.
Which of the following is false ?
A) {1} ∈ A
B) {1, 2} ⊆ A
C) {1, 2} ∈ A
D) None
Answer:
D) None

Question 35.
If A = {1, 2, 3, 4}, B = {2, 4,6, 8} then A – B =
A) {6, 8}
B) {1, 2}
C) {1, 3}
D) None
Answer:
C) {1, 3}

Question 36.
If n(A ∪ B) = 8, n (A) = 6, n(B) = 4 then n (A ∩ B) = …….
A) 2
B) 4
C) 6
D) 8
Answer:
A) 2

Question 37.
Let A, B are two sets such that n(A) = 5, n(B) = 7 then the maximum number of elements in A ∪ B is
A) 7
B) 9
C) 12
D) None
Answer:
C) 12

Question 38.
If A = {1, 2, 3, 4 }, then the cardinality of set A is
A) 3
B) 4
C) 5
D) 6
Answer:
B) 4

Question 39.
If A, B are disjoint sets such that n(A) = 4 and n(A∪B) = 7, then n(B) = ……..
A) 4
B) 11
C) 3
D) 20
Answer:
C) 3

Question 40.
An object of a set is called
A) Subject
B) Number
C) Alphabet
D) Element
Answer:
D) Element

Question 41.
The symbol used for ‘belongs to’ is
A) ⊂
B) ⊆
C) ∈
D) \(\notin\)
Answer:
C) ∈

Question 42.
The set of all real numbers is
A) ϕ
B) Finite set
C) Infinite set
D) None
Answer:
C) Infinite set

Question 43.
The number of elements in the empty set is
A) 0
B) ϕ
C) 1
D) ∞
Answer:
A) 0

Question 44.
If A = {1, 2, 2, 1, 3, 4, 3, 4}, then n(A) =
A) 0
B) 4
C) 8
D) 20
Answer:
B) 4

Question 45.
If A ⊂ B, then A ∪ B = ………..
A) ϕ
B) μ
C) A
D) B
Answer:
D) B

Question 46.
A ∩ ϕ = ………
A) ϕ
B) µ
C) A
D) A^c
Answer:
A) ϕ

Question 47.
The German mathematician who developed the theory of sets ………
A) Bhaskara
B) Cayley
C) George Cantor
D) None
Answer:
C) George Cantor

Question 48.
A set is a …….. of objects.
A) well defined collection
B) collection
C) elements
D) none
Answer:
A) well defined collection

Question 49.
The objects in the set are called ……….. of the set.
A) elements
B) members
C) both A & B
D) false
Answer:
C) both A & B

Question 50.
Roster form of the set of natural numbers less then 6 is ……….
A) {4, 5, 6}
B) {1, 2, 3}
C) {2, 3, 4}
D) {1,2, 3, 4, 5}
Answer:
D) {1,2, 3, 4, 5}

Question 51.
The set formed from the letters of the word “SCHOOL” is ……
A) {S, O, H}
B) {H, O, L}
C) {S, C, H}
D) {S, C, H, O, L}
Answer:
D) {S, C, H, O, L}

Question 52.
Roster form is also called ……. form.
A) list
B) set
C) number
D) none
Answer:
A) list

Question 53.
Describing a set by same property common to all its elements is called …….. or ………
A) set builder form
B) rule form
C) both A & B
D) none
Answer:
C) both A & B

Question 54.
A = {2, 4, 6, 8, 10} then its rule form is ……..
A) A = {x² / x ∈ N}
B) A = {2x / x is odd, x ≤ 20}
C) A = {x³ / x ∈ N}
D) A = {x / x is an even number, x ≤ 10}
Answer:
D) A = {x / x is an even number, x ≤ 10}

Question 55.
If B = {1, 7, 2, 0, 6} then n(B) = …….
A) 5
B) 6
C) 7
D) 9
Answer:
A) 5

Question 56.
n (ϕ) = ……….
A) n
B) ϕ
C) 0
D) 9
Answer:
C) 0

Question 57.
Every set is ………. of itself.
A) subset
B) proper set
C) power set
D) none
Answer:
A) subset

Question 58.
If A ⊂ B and A ≠ B then ‘A’ is called the ……… of B.
A) subset
B) proper subset
C) power set
D) none
Answer:
B) proper subset

Question 59.
In set Builder form, the letter x denotes any …….. that belongs to the set.
A) constant
B) element
C) arbitrary element
D) none
Answer:
C) arbitrary element

Question 60.
In the rule form, the sland bar stands for ……….
A) subset
B) such that
C) belongs
D) all
Answer:
B) such that

Question 61.
2 is ……….. of set of natural numbers.
A) power
B) proper
C) subset
D) an element
Answer:
D) an element

Question 62.
-3 is …….. of the set of whole numbers.
A) proper
B) power
C) element
D) not an element
Answer:
D) not an element

Question 63.
0 ……….. to set of whole numbers.
A) does not belong
B) belong
C) subset
D) power set
Answer:
B) belong

Question 64.
A = {1, 2, 7, 10} then 7 …….. A.
A) ⊂
B) ∈
C) \(\notin\)
D) none
Answer:
B) ∈

Question 65.
A = {1, 2, 7,10} then 4 …… A.
A) \(\supset\)
B) ∈
c) ⊂
D) \(\notin\)
Answer:
D) \(\notin\)

Question 66.
“0 does not belong to the set of natural numbers” we write the statement symbolically as ………..
A) 0 \(\notin\) N
B) 0 ∈ N
C) 0 ⊂ N
D) none
Answer:
A) 0 \(\notin\) N

Question 67.
Set builder form of D = {1, \(\frac{1}{2}\), \(\frac{1}{3}\), \(\frac{1}{4}\), \(\frac{1}{5}\), \(\frac{1}{6}\)} is ………..

Answer:
B) k = {\(\frac{x}{x}\) = \(\frac{1}{n^3}\), n ∈ N}

Question 68.
B = {\(\frac{x}{x}\) + 3 = 6}, B = …………
A) {0, 1, 3}
B) {7, 0}
C) {0, 3}
D) {3}
Answer:
D) {3}

Question 69.
A ……….. is a set with no elements in it.
A) inifinite set
B) finite set
C) null set
D) none
Answer:
C) null set

Question 70.
The null set is sometimes denoted as …………
A) empty set
B) void set
C) both A & B
D) none
Answer:
C) both A & B

Question 71.
Empty set is denoted by ………..
A) {ϕ}
B) {0}
C) N
D) ϕ
Answer:
D) ϕ

Question 72.
{0} is a set contains the element
A) 0
B) ϕ
C) {ϕ}
D) none
Answer:
A) 0

Question 73.
A set with only are element is known as ……. set.
A) Double
B) Singleton
C) Tri
D) None
Answer:
B) Singleton

Question 74.
Number of elements in a singleton set is …….
A) 0
B) 2
C) 7
D) 1
Answer:
D) 1

Question 75.
A = {x/x + 4 = 4} then A = ……
A) {4}
B) {0}
C) {0, 4}
D) {0, 7}
Answer:
B) {0}

Question 76.
B = {x / x ∈ N and x < 1000} is a …….. set.
A) finite
B) infinite
C) singleton
D) empty
Answer:
A) finite

Question 77.
If in two sets A and B, every element of A is in B and every element of B is in A. Then we write it as ………..
A) A ≠ B
B) A < B C) A > B
D) A = B
Answer:
D) A = B

Question 78.
A ≠ B means, set A and B do not contains same elements. This is
A) false
B) true
C) can’t be determined
D) none
Answer:
B) true

Question 79.
The number of elements in a set is called the ……. of the set.
A) cardinal
B) ordinal
C) true
D) all the above
Answer:
A) cardinal

Question 80.
If B = {1, 7, 2, 0, 6} then n(B) = ……..
A) 7
B) 0
C) 6
D) 5
Answer:
D) 5

Question 81.
If every element of A is also an element of B then we write this as ……
A) A < B
B) B < A
C) A ⊂ B
D) B ⊂ A
Answer:
C) A ⊂ B

Question 82.
If A = {1, 2, 3} and B = {1, 2, 3, 4} then we say A is a …… of B.
A) subset
B) superset
C) equal
D) none
Answer:
A) subset

Question 83.
In the above question B is ……… of A.
A) subset
B) superset
C) superset
D) all the above
Answer:
C) superset

Question 84.
A is not a subset of B if A contains ……… which is not in B.
A) equal
B) at least one element
C) 2
D) none
Answer:
B) at least one element

Question 85.
{x/x is a student of your school) is in ………. form.
A) Roster
B) Singleton
C) Set Builder
D) None
Answer:
C) Set Builder

Question 86.
{2, 4, 6, 8, 10} is an example of …….. set.
A) finite
B) infinite
C) singleton
D) two
Answer:
A) finite

Question 87.
{x/x is a natural number} is a ……….. set.
A) finite
B) infinite
C) singleton
D) none
Answer:
B) infinite

Question 88.
{x/x≠x} is a ……. set.
A) empty
B) infinite
C) singleton
D) none
Answer:
A) empty

Question 89.
A = {1, 2, 3}, B = {3, 4, 5} then A ∩ B = ……….
A) 3
B) {1, 2}
C) {4, 5}
D) {3}
Answer:
D) {3}

Question 90.
A = {a, b, c}, B = {c, a, b} then …………
A) A≠B
B) A = B
C) A ⊂ B
D) none
Answer:
B) A = B

Question 91.
A = {1, 2, 7}, B = {2, 1} then ………
A) A ⊂ B
B) B ⊂ A
C) A = B
D) none
Answer:
B) B ⊂ A

Question 92.
A ⊂ B then A – B = ……..
A) ⊂
B) B
C) A
D) ϕ
Answer:
D) ϕ

Question 93.
A – ϕ = ……….
A) A
B) ϕ
C) μ
D) none
Answer:
A) A

Question 94.
A ∪ A’ = ………..
A) A
B) ϕ
C) A
D) A’
Answer:
B) ϕ

Question 95.
μ’ = …………
A) A
B) μ
C) ϕ
D) none
Answer:
C) ϕ

Question 96.
A = {1, 2, 3}, B = {12, 0, 5} then A – B = ………
A) B
B) A
C) {5}
D) none
Answer:
B) A

Question 97.
A ∪ ϕ = ………….
A) A
B) B
C) ϕ
D) μ
Answer:
A) A

Question 98.
ϕ’ = ………..
A) B
B) A
C) μ
D) 0
Answer:
B) A

Question 99.
{2, 6, 10} ∩ {8, 9, 11, 12, 13} = ………..
A) {2}
B) {1, 2}
C) {13, 1}
D) ϕ
Answer:
D) ϕ

Question 100.
n(A) = 4 then n(p(A)) = …….
A) 12
B) 13
C) 15
D) 16
Answer:
D) 16

Question 101.
A – (A – B) = ……….
A) A ∩ B
B) ϕ
C) A ∪ B
D) B
Answer:
A) A ∩ B

Question 102.
(A’)’ = …………
A) A’
B) A
C) ϕ
D) none
Answer:
B) A

Question 103.
If A ⊂ B, then A – B = ………..
A) μ
B) B
C) A
D) ϕ
Answer:
D) ϕ

Question 104.
If A ⊂ B then A ∪ (B – A) = ………
A) B
B) A
C) ϕ
D) none
Answer:
A) B

Question 105.
W – {0} = ……..
A) R
B) A
C) Z
D) Q
Answer:
B) A

Question 106.
If A ⊂ B, B ⊂ C then ………
A) B = C
B) A = B
C) C ⊂ A
D) A ⊂ C
Answer:
D) A ⊂ C

Question 107.
Cardinal number of null set is ……
A) 4
B) ϕ
C) 0
D) none
Answer:
C) 0

Question 108.
A’ – B’ = ……..
A) A – B’
B) A’ – B
C) B – A
D) A – B
Answer:
C) B – A

Question 109.
If A = {1, 2, 3}, B = {3, 4, 5} then A ∆ B = ……….
A) {0}
B) {1, 2}
C) {7}
D) none
Answer:
D) none

Question 110.
A = ϕ, B = ϕ then A ∪ B = …………..
A) μ
B) ϕ
C) cant be determined
D) None
Answer:
B) ϕ

Question 111.
A ∩ B = ϕ then n (A ∩ B) = ………..
A) 7
B) 9
C) 3
D) none
Answer:
D) none

Question 112.
A ∪ B = A ∩ B then ……………….
A) A = B
B) A ≠ B
C) A ⊂ B
D) B ⊂ C
Answer:
A) A = B

Question 113.
μ’ = ϕ is called ……….. law.
A) Identity
B) Associative
C) Inverse
D) Complementary
Answer:
D) Complementary

Question 114.
A’ = B then A ∪ B = …….
A) A
B) μ
C) ϕ
D) none
Answer:
D) none

Question 115.
ϕ ∆ ϕ = ………..
A) μ
B) ϕ
C) {0}
D) none
Answer:
B) ϕ

Question 116.
A ∪ A = A is called ……… law.
A) idempotent
B) inverse
C) complete
D) identity
Answer:
A) idempotent

Question 117.
A ∪ B = B if …………
A) A \(\supset\)
B) A ⊂ B
C) A = B
D) none
Answer:
B) A ⊂ B

Question 118.
A = ϕ, B = ϕ then A ∩ B = ………
A) {6, 1}
B) {0}
C) μ
D) ϕ
Answer:
D) ϕ

Question 119.
n(A) = 10, n(B) = 4, n(A∩B) = 2 then n(A∪B) = ……….
A) 11
B) 16
C) 10
D) 12
Answer:
D) 12

Question 120.
(A ∪ B)’ = ………..
A) A’ ∩ B’
B) A’∪B
C) A’ ∩B
D) A ∩ B
Answer:
A) A’ ∩ B’

Question 121.
(A – B) ∪ {A – C) = ……..
A) (A – B) ∪ C
B) (A – B) ∩ C
C) (A – B) – C
D) none
Answer:
D) none

Question 122.
n(A) = 3 then number of proper subsets of A is ………
A) 10
B) 9
C) 7
D) 8
Answer:
C) 7

Question 123.
A ∩ B = ϕ then B ∩ A’ = ……….
A) μ
B) A
C) ϕ
D) B
Answer:
D) B

Question 124.
A ∪ (B ∩ C) = ……..
A) (A ∪ B) ∩ (A ∪ C)
B) (A∩B)∪(A∩C)
C) (A∪B)∩C
D) none
Answer:
A) (A ∪ B) ∩ (A ∪ C)

Question 125.
A = {all primes less than 20}
B = {all whole numbers less than 10} then
A∩B = ………….
A) {2, 3, 5, 7, 10}
B) {2, 8, 9}
C) {2, 3, 5, 7}
D) {2, 4, 6}
Answer:
C) {2, 3, 5, 7}

Question 126.
In the above problem A – B = ……….
A) {11, 13, 17, 19}
B) {1, 3, 7, 19}
C) {13, 17, 10}
D) none
Answer:
A) {11, 13, 17, 19}

Question 127.
N(A∪B) = 51, n(A) = 20, n(A∩B) = 13, then n(B) =
A) 80
B) 44
C) 40
D) 39
Answer:
B) 44

Question 128.
The identity element under union of sets of ………..
A) μ
B) {0}
C) {ϕ}
D) none
Answer:
C) {ϕ}

Question 129.
μ ∪ ϕ = ………..
A) ϕ
B) {0}
c) {ϕ}
D) μ
Answer:
D) μ

Question 130.

This venn – diagram represents ……..
A) A ∩ B
B) A – B
C) A ∪ B
D) A Δ B
Answer:
A) A ∩ B

Question 131.
N ∩ W = ……
A) Q
B) W
C) N
D) {0}
Answer:
C) N

Question 132.
If A and B are disjoint sets then n (A ∪ B) = ………
A) n(A) – n(B)
B) n(A) + n(B)
C) \(\frac{n(A)}{n(B)}\)
D) none
Answer:
B) n(A) + n(B)

Question 133.
From the venn diagram A ∪ B = ………..

A) {1, 2, 3}
B) {1, 2, 4, 5}
C) {6, 7, 10}
D) none
Answer:
D) none

Question 134.
Identity element under intersection of sets is ………
A) {0}
B) μ
C) ϕ
D) none
Answer:
B) μ

Question 135.
Which of the following is true ?
A) A – B ≠ B – A
B) A ∪ ϕ = A
C) μ’ = μ
D) all
Answer:
A) A – B ≠ B – A

Question 136.
A is the set of factors of 12. Which are of the following is not a member of A ?
A) 9
B) 10
C) 12
D) 5
Answer:
D) 5

Question 137.
If the number of proper subsets of a given set is 31 then the set contains elements.
A) 7
B) 6
C) 5
D) 10
Answer:
C) 5