Practice the AP 10th Class Maths Bits with Answers Chapter 2 Sets on a regular basis so that you can attempt exams with utmost confidence.

## AP State Syllabus 10th Class Maths Bits 2nd Lesson Sets with Answers

Question 1.

Which type of set of human being that reside on moon is ……………….

Answer:

null set

Question 2.

Write the number of subsets of the null set Φ.

Answer:

1

Question 3.

Ifn(A) = 8, n(B) = 3, n(A ∩ B) = 2, then find n(A ∪ B).

Answer:

9

Explanation:

n(A∪B) = n (A) + n (B) – n (A ∩ B)

= 8 + 3-2 = 9

Question 4.

The number of subsets of a set is 16, then find the set has ………… elements.

Answer:

4

Explanation:

2^{n} = 16 = 2^{4}

⇒ no. of elements in the set = 4

Question 5.

Write the number of subsets of the set A = {l, 2,3, 4}.

Answer:

16

Explanation:

n (A) = 4, no. of subsets = 2^{n} = 2^{4} = 16

Question 6.

If A⊂ B, n(A) = l2and n(13) = 20, then find the value of n (B – A).

Answer:

8

Explanation:

A ⊂ B, son (B – A) = 20- 12 .= 8

Question 7.

Roster form of (x: x is a prime number and a divisor of 6).

Answer:

{2,3}

Question 8.

Write an example for finite set in your own.

Answer:

{x/x∈N and x^{2} = 9}

Question 9.

If A⊂B,n(A) = 4 and n(B) = 6,then find n(A∪ B).

Answer:

6

Explanation:

A ⊂ B, so n (A ∪ B) = n (B) = 6

Question 10.

If A⊂B, then A∩B is

Answer:

A

Explanation:

A⊂B, so A∩B = A

Question 11.

If the union of two sets is one of the set itself, write the relation between the two sets.

Answer:

One set is a subset of other set.

Question 12.

The following venn diagram indicates

Answer:

A⊂B

Question 13.

If A From the venn diagram, find A ∪ B.

Answer:

{5, , 7, 8}

Question 14.

If A = {x : x is a letter in the word EX¬AMINATION}, then write its roster form.

Answer:

A = {e, x, m, i, n, a, t, o}

Question 15.

If A = {x : x is a letter in the word HEADMASTER}; then write its ros-ter form.

Answer:

A — {h, e, a, d, m, s, t, r}

Question 16.

If n (A) = 12 and n (A ∩ B) = 5, then find n (A – B).

Answer:

7

Explanation:

n (A – B) = n(A) – n(A∩B) = 12 – 5 = 7

Question 17.

The following venn diagram indicates

Answer:

A, B are disjoint sets.

Question 18.

The shaded region in the given figure shows.

Answer:

μ – B = B’

Question 19.

Write the relation between sets in the following venn diagram.

Answer:

A ∩ B = Φ

Question 20.

If A ={1,2, 3}, B = (3,4, 5), then find A Δ B.

Answer:

A Δ B = {1,2, 4, 5}

Explanation:

A Δ B = (A ∪ B) – (A ∩ B)

= {1, 2, 3, 4, 5}- {3} = {1,2, 4, 5}

Question 21.

(A’)’is equal to …………….

Answer:

A

Question 22.

An object of a set is called ……………..

Answer:

Element

Question 23.

2 is ………………. of set of natural numbers.

Answer:

An element

Question 24.

Number of elements in a singleton set is …………………..

Answer:

1

Question 25.

If A, B are disjoint sets such that n (A) = 4 and n (A ∪ B) = 7, then find n(B).

Answer:

3

Explanation:

n(A∪B) = n (A) + n (B) – n (A ∩ B)

⇒ 7 = 4 + n (B) – 0

⇒ n(B) = 7 – 4 = 3

Question 26.

‘O’ is to set of whole numbers.

Answer:

belong

Question 27.

n (A) = 4, then write n(p(A)).

Answer:

16

Explanation:

n(P(A)) = 2^{n} = 2^{4} = 16

Question 28.

If A = {1, 2, 3} and B = {1, 2, 3, 4}, then we say A is a …………….. of B.

Answer:

Subset

Question 29.

Φ is equal to A.

Answer:

μ

Question 30.

A set is a ……………… of objects.

Answer:

Well defined collection.

Question 31.

{2, 4,6, 8, 10} is an example of which type of set ?

Answer:

Finite

Question 32.

If A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, then find A – B.

Answer:

{1,3}

Question 33.

A = {2, 4, 6, 8, 10}, then write its rule form.

Answer:

A = {x / x is an even number, x ≤ 10}

Question 34.

If B = {1, 7, 2, 0, 6}, then find n(B).

Answer:

5

Question 35.

A – (A -B) is equal to ……………..

Answer:

A ∩ B

Question 36.

The objects in the set are called ……………….. of the set.

Answer:

Elements

Question 37.

Let A, B are two sets such that n (A) = 5, n(B) = 7, then write the maximum number of elements in A ∪ B.

Answer:

12

Question 38.

Empty set is denoted by ………………..

Answer:

Φ

Question 39.

Write A Δ B.

Answer:

(A – B) ∪

(B – A) (or) (A∪B)-(A ∩ B)

Question 40.

A = {1, 2, 3}, B = {3, 4, 5}, then find A ∩ B.

Answer:

{3}

Question 41.

– 3 is of the set of whole numbers.

Answer:

not an element

Question 42.

If n(A ∪ B) = 8, n(A) = 6, n(B) = 4, then find n(A ∩ B).

Answer:

2

Question 43.

The number of elements in a set is called the…………….of the set.

Answer:

Cardinal number

Question 44.

A ∪ Φ is equal to …………………

Answer:

A

Question 45.

{x / x ≠ x} is which type of set ?

Answer:

Empty

Question 46.

B = {x/x ∈ N and x < 1000} is a ……………type of set.

Answer:

Finite

Question 47.

Write the symbol used for belongs to’.

Answer:

∈

Question 48.

n (Φ) is equal to ………………..

Answer:

0

Question 49.

Write (2, 6, 10} ∩ (8, 9, 11, 12, 13}.

Answer:

Φ

Question 50.

{x / x is a student of your school} is in which form ?

Answer:

Set Builder

Question 51.

Every set is ……………. of itself.

Answer:

Subset

Question 52.

A = {1, 2,7, 10}, then use symbol be-tween 7 and A.

Answer:

∈

Question 53.

If A = {1, 2, 3, 4}, then find the cardi-nality of set A.

Answer:

4

Question 54.

A≠B means, set A and B do not contains same elements. This statement is true (or) false.

Answer:

True

Question 55.

A = {1, 2, 3}, B = {12, 0, 5}, then find A-B.

Answer:

A

Question 56.

A = {x / x + 4 = 4}, then write Roster form of A.

Answer:

{0}

Question 57.

Which type of set has no elements in it ?

Answer:

Null set

Question 58.

If A ∪ B = A ∪ C and A ∩ B = A ∩ C, then write the relation between these sets.

Answer:

B = C

Question 59.

A set with only one element is known as ……………. set.

Answer:

singleton

Question 60.

The set of all real numbers is, which type of set ?

Answer:

Infinite set

Question 61.

Roster form of B = \(\left\{\frac{x}{x}+3=6\right\}\), B = ?

Answer:

{3}

Question 62.

‘μ’ is equal to

Answer:

Φ

Question 63.

If A ⊂ B and A ≠ B, then A’ is called the ………………. of B.

Answer:

Proper subset

Question 64.

{x / x is a natural number} is which type of set ?

Answer:

Infinite

Question 65.

Write the number of elements in the empty set.

Answer:

0

Question 66.

The null set is sometimes denoted as .

Answer:

{} = Φ

Question 67.

If in two sets A and B, every element of A is in B and every element of B is in A, then write it as

Answer:

A = B

Question 68.

Another name to Roster form is ……………….

Answer:

List

Question 69.

A’ – B’ is equal to

Answer:

B-A

Question 70.

If every element of A is also an element of B, then write this symboliically.

Answer:

A⊂B

Question 71.

A ⊂ B, then find A – B.

Answer:

Φ

Question 72.

“0 does not belong to the set of natural numbers”. Write the statement sym¬bolically.

Answer:

0 ∉ N

Question 73.

A = {1,2, 4}, B = {3, 5, 6}, then write the relation.

Answer:

A ∩ B = Φ

Question 74.

If A ⊂ B, then find A ∪ B.

Answer:

B

Question 75.

If B = {1,7, 2, 0,6}, then find n(B).

Answer:

5

Question 76.

Write Roster form of the set of natu¬ral numbers less than 6.

Answer:

(1, 2, 3, 4, 5}

Question 77.

If A ⊂ B, then find A-B.

Answer:

Φ

Question 78.

A ∪ Φ is equal to ……………

Answer:

A

Question 79.

A ∪ B = B ∪ A is called ……………. law.

Answer:

Commutative

Question 80.

If A = {1, 2, 2, 1, 3, 4, 3, 4}, then find n(A).

Answer:

4

Question 81.

Write cardinal number of null set.

Answer:

0

Question 82.

K = {x/x is a prime number less than 13}. Write list form of K.

Answer:

K= {2, 3, 5, 7, 11}

Question 83.

W – {0} is equal to …………………

Answer:

N

Question 84.

In the rule form, the slant bar stands for

Answer:

such that

Question 85.

A = {a, b, c}, B = {c, a, b}, then write the relation between A and B.

Answer:

A – B

Question 86.

Write the set formed from the letters of the word “SCHOOL “.

Answer:

{S, C, H, O, L}

Question 87.

A = {1, 2, 7}, B = {2, 1}, then write the relation between A and B.

Answer:

B⊂A

Question 88.

If A ⊂ B, B ⊂ C, then write the relation between A and C.

Answer:

A ⊂ C

Question 89.

If A ⊂ B, then find A∪(B – A).

Answer:

B

Question 90.

Write the set builder form of D = \(\left\{1, \frac{1}{2}, \frac{1}{3} ; \frac{1}{4}, \frac{1}{5}, \frac{1}{6}\right\}\)

Answer:

D = {x / x ∈ 1/n ,n ∈ N,n < 7}

Question 91.

In set builder form, the letter “X” denotes any………… that belongs to the set.

Answer:

Arbitrary element.

Question 92.

Write the Roster form of the set of multiples of 5 which lie between 25 and 50 is

Answer:

{30, 35, 40, 45}

Question 93.

Write the name of German mathemati¬cian who developed the theory of sets.

Answer:

George Cantor.

Question 94.

N∩W is equal to ………………..

Answer:

N

Question 95.

A = Φ, B = Φ, then find A∩B.

Answer:

Φ

Question 96.

Write the identity element under union of sets.

Answer:

Φ

Question 97.

A ∩ B = Φ, then find B ∩ A’.

Answer:

B

Question 98.

A = {all primes less than 20}

B = {all whole numbers less than 10}, then find A∩B.

Answer:

{2,3, 5, 7}

Question 99.

μ’ = Φ is called …………….. law.

Answer:

Complementary

Question 100.

A ∪ A = A is called……………law.

Answer:

Idempotent.

Question 101.

If A and B are disjoint sets, then write n (A ∪ B).

Answer:

n (A) + n (B)

Explanation:

n (A ∪ B) = n (A) + n (B)

Question 102.

If A = Φ, B = Φ, then find A∪B.

Answer:

Φ

Question 103.

n (A) = 3, then write the number of proper subsets of A.

Answer:

7

Explanation:

Proper subsets are 2^{n} – 1 = 2^{3} – 1

= 8 – 1

= 7

Question 104.

A ∪ B = A ∩ B, then write the relation between A and B.

Answer:

A = B

Question 105.

n (A ∪ B) = 51, n (A) = 20, n (A ∩ B) = 13, then find n (B).

Answer:

44

Explanation:

n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

⇒ 51 = 20 + n(B)- 13

⇒ 31 + 13 = n(B) = 44

Question 106.

A’ = B, then find A ∪ B.

Answer:

μ

Explanation:

A’= B ⇒ μ – A = B

⇒ A u B = μ

Question 107.

n (A) = 10, n (B) = 4, n (A ∩ B) = 2, then find n (A ∪ B).

Answer:

12

Question 108.

μ ∪ Φ is equal to

Answer:

μ

Question 109.

If A ∩ B = Φ then find n (A ∩ B).

Answer:

n (A) + n (B)

Question 110.

Write the identity element under intersection of sets.

Answer:

μ

Question 111.

A∪B = B, then write the relation between A and B.

Answer:

A⊂B

Question 112.

The given venn diagram represents.

Answer:

AΔB

Question 113.

Φ Δ Φ is equal to

Answer:

Φ

Question 114.

(A ∪ B)’ is equal to

Answer:

A’ ∩ B’

Explanation:

(A ∪ B)’ = A’∩B’

Question 115.

Draw the venn diagram of A – B.

Answer:

Question 116.

If the number of proper subsets of a given set is 31, then how many ele-ments the set contains ?

Answer:

5

Explanation:

2^{n} – 1 = 31 ⇒ 2^{n} = 32 = 2^{5}

∴ no. of elements are 5.

Question 117.

Write the intersection of set of ratio-nal numbers and set of irrational num¬bers.

Answer:

Real numbers

Question 118.

This venn diagram represents

Answer:

A∩B

Question 119.

From the venn diagram, write the set A∪B.

Answer:

A ∪ B = {1, 2, 4, 5, 6, 7, 10}

Explanation:

A ∪ B = {1,2, 4, 5, 6, 7, 10}

If A = {x : x is a natural number}

B = {x : x is an even natural number}

C = {x : x is an odd natural number) and

D = {x : x is a prime number}

Question 120.

Find A∩B.

Answer:

A∩B = (1, 2, 3, 4, } ∩ (2, 4, 6, 8…………… }

= {2,4,6, 8, ….} = B{∵B⊂A}

Question 121.

Find A ∩C.

Answer:

A ∩ C = {1, 2, 3,4, …} ∩ {1, 3, 5, 7,…} = (1,3, 5, 7,…} = C(∵C⊂A}

Question 122.

Find A ∩D.

Answer:

A∩D = {1,2, 3, 4, …} ∩ {2, 3,5,7,…} = {2, 3, 5, 7,…} = D{∵ D⊂A)

By observing the below diagram and answer the following questions :

Question 123.

Find A∪B.

Answer:

A∪B = {2, 3, 4, 5, 6} ∪ {7, 8, 9, 10} = {2,3,4,5,6,7,8,9,10}

Question 124.

Find A∩B.

Answer:

A∩B = {2, 3, 4, 5, 6} ∩ {7, 8, 9, 10}

= { } = Φ

Question 125.

Find A Δ B.

Answer:

A Δ B = (A ∪ B) – (A ∩ B) = A ∪ B . { ∵ A ∩ B = Φ}

By observing the below diagram and answer the following questions.

Question 126.

What do you observes in P and Q ?

Answer:

There are no common elements

Question 127.

Name the type of sets P and Q.

Answer:

P and Q are disjoint sets.

Question 128.

Write the relation between P and Q.

Answer:

P ∩ Q = Φ

Question 129.

Define disjoint sets.

Answer:

There is no common elements in any two sets such type of sets are called disjoint sets.

By observing the below information and answer the following questions.

D = The set of all letters in the word TRIGONOMETRY

Question 130.

Write the Roster form of set ‘D’.

Answer:

D = {T, R, I, G, O, N, M, E, Y}

Question 131.

Write the cardinal number of set D.

Answer:

n (D) = 9

By observing the below diagram and answer the following questions.

Question 132.

Find n(A).

Answer:

n (A) = 2

Question 133.

Find n(B).

Answer:

n (B) = 1

Question 134.

Find n(A ∩ B).

Answer:

n(A ∩ B) = Φ

Question 135.

Find n(A ∪ B).

Answer:

n(A ∪ B) = 3

Question 136.

Write the relation between n (A), n (B), n (A ∩ B) and n (A ∪ B).

Answer:

n (A) + n (B) = n(A∪B) + n(A∩B)

1 + 2 = 3 + 0 = 3

Write the correct matching options.

Question 140.

Roster form

A) {a, e, i, o, u} []

B) {2, 5, 10, 17} []

Choose the correct answer satistying the following statements.

Question 137.

Statement (A): If A = {1,2,3, 4, 5,6}, B = {7,8,9, 10, 11} and C = {6,8, 10, 12,14}, then A and B are disjoints sets.

Statement (B) : Two sets A and B are said to be disjoint, if A ∩ B = Φ

i) Both A and B are true

ii) A’ is true, ‘B’ is false

iii) A is false,’B’is true

iv) Both A and B are false

Answer:

i)

Question 138.

Statement (A) : The set of all rect-angles in contained in the set of all squares.

Statement (B) : The sets P = {a} and B = {{a}} are equal.

i) Both A and B are true

ii) A is true, ‘B’ is false

iii) A’ is false, ‘B’ is true

iv) Both A and 6 are false

Answer:

ii)

Question 139.

Statement (A) : For any two sets A and B, we have A – B = {x : x ∉ A and x∈B}

Statement (B) : For any two sets A and B, we have A-B = {x:x∈A and x∉B) andB-A = {x:x ∈ B and x ∉ A}

i) Both A and B are true

ii) A’ is true, ‘B’ is false

iii) A’ is false, ‘B’ is true

iv) Both A and B are false

Answer:

iii)

Write the correct matching options.

Question 140.

Roster form

Answer:

A – (i), B – (iv).

Question 141.

Answer:

A – (iii), B – (ii).

Question 142.

Answer:

A – (iv), B – (iii).

Question 143.

Answer:

A – (i), B – (ii).

Question 144.

Answer:

A – (ii), B – (iii).

Question 145.

Answer:

A – (i), B – (iv).

Question 146.

If A = {1,2,3} and Φ = { }, find A∩Φ

Answer:

Φ

Question 147.

Find n(A ∪ B) from the figure

Answer:

5

Question 148.

How many subsets does a set of three distinct elements have ?

Answer:

8 sub-sets

Question 149.

If A = {1,2,3} andB = {2,4,6}. What is n(A ∪ B) ?

Solution:

A = {1, 2, 3}, B = {2, 4, 6}

A∪B = {1, 2, 3}∪{2, 4,6} = {1,2,3,4,61

n(A ∪ B) = 5