AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 2 Sets Ex 2.1 Textbook Questions and Answers.

## AP State Syllabus SSC 10th Class Maths Solutions 2nd Lesson Sets Exercise 2.1

### 10th Class Maths 2nd Lesson Sets Ex 2.1 Textbook Questions and Answers

Question 1.

Which of the following are sets? Justify your answer.

i) The collection of all the months of a year beginning with die letter “J”.

ii) The collection of ten most talented writers of India.

iii) A team of eleven best cricket batsmen of the world.

iv) The collection of all boys in your class.

v) The collection of all even integers.

Answer:

i) There are 3 months as January, June and July beginning with letter ‘J’. Therefore, it is a well defined collection of months and hence it is a set.

ii) The concept of talented writers of India is vague, since there is no rule given for deciding whether a particular writer is talented or not.

Hence, the given collection is not a set.

iii) A team of eleven best cricket batsmen of the world is vague, since there is no rule given for deciding whether a particular batsman is the best.

Hence, the given collection is not a set.

iv) The collection of all boys in my class is well defined. Hence, the given collection is a set.

v) The collection of all even integers i.e., (2, 4, 6, 8, ……) is well defined.

Hence, the given collection is a set.

Question 2.

If A = {0, 2, 4, 6}, B = {3, 5, 7} and C = {p, q, r} then fill the appropriate symbol, ∈ or ∉ in the blanks.

i) 0 ….. A

ii) 3 ….. C

iii) 4 ….. B

iv) 8 ….. A

v) p ….. C

vi) 7 ….. B

Answer:

i) ∈

ii) ∉

iii) ∉

iv) ∉

v) ∈

vi) ∈

Question 3.

Express the following statements using symbols.

i) The elements ‘x’ does not belong to ‘A’.

ii) ‘d’ is an element of the set ‘B’.

iii) ‘1’ belongs to the set of Natural numbers N.

iv) ‘8′ does not belong to the set of prime numbers P.

Answer:

i) x ∉ A

ii) d ∈ B

iii) 1 ∈ N

iv) 8 ∉ P

Question 4.

State whether the following statements are true or false. Justify your answer.

i) 5 ∉ set of prime numbers

ii) S = {5, 6, 7} implies 8 ∈ S.

iii) -5 ∉ W where ‘W’ is the set of whole numbers.

iv) \(\frac{8}{11}\) ∈ Z

where ‘Z’ is the set of integers.

Answer:

i) False

ii) False

iii) True

iv) False

Question 5.

Write the following sets in roster form.

i) B = {x : x is a natural number smaller than 6}.

ii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}.

iii) D = {x : x is a prime number which is a divisor of 60}.

iv) E = {x : x is an alphabet in BETTER}.

Answer:

i) B = {1, 2, 3, 4, 5}

ii) C = {17, 26, 35, 44, 53, 62, 71}

iii) D = {5, 3}

iv) E = {B, E, T, R}

Question 6.

Write the following sets in the set – builder form.

i) {3, 6, 9, 12}

ii) {2, 4, 8, 16, 32}

iii) {5, 25, 125, 625}

iv) {1, 4, 9, 16, 25, …, 100}

Answer:

i) A = {x : x is multiple of 3 and less than 13}

ii) B = {x : x = 2^{P}, 0 < P < 6, P ∈ N}

iii) C = {x : x = 5^{P}, 0 < P < 5, P ∈ N}

iv) D = {x : x = P^{2}, 0< P < 11, P ∈ W}

Question 7.

Write the following sets in roster form.

i) A = {x: x is a natural number greater than 50 but smaller than 100}

ii) B = {x : x is an integer, x^{2} = 4}

iii) D = {x : x is a letter in the word “LOYAL”}

Answer:

i) A = {51, 52, 53, ……. , 98, 99}

ii) B = {+2, -2}

iii) D = {L, O, Y, A}

Question 8.

Match the roster form with set builder form.

i) {1, 2, 3, 6} ( ) a) {x : x is a prime number and a divisor of 6}

ii) {2, 3} ( ) b) {x : x is an odd natural number smaller than 10}

iii) {M, A, T, H, E, I, C, S} ( ) c) {x : x is a natural number and divisor of 6}

iv) {1, 3, 5, 7, 9} ( ) d) {x : x is a letter of the word MATHEMATICS}

Answer:

i) c

ii) a

iii) d

iv) b