Students can practice TS 10th Class Maths Solutions Chapter 2 Sets Ex 2.3 to get the best methods of solving problems.

## TS 10th Class Maths Solutions Chapter 2 Sets Exercise 2.3

Question 1.

Which of the following sets are equal ?

a) A = {x : x is a letter in the word FOLLOW’}

b) B = {x : x is a letter in the word ‘FLOW’}

c) C = {x : x is a letter in the word ‘WOLF’}

Answer:

a) Writing the given set in the roaster form, we have A = {F, O, L, W}

b) Writing the given set in the roaster form, we have B = {F, L, O, W}

c) Writing the given set in the roaster form, we have C = {W, O, L, F}

Therefore, A, B, C are equal sets.

[∴ The sets A, B, C have exactly the same elements]

Question 2.

Consider the following sets and fill up the blank in the statement given below with = or ≠ so as to make the statement true.

A = {1, 2, 3};

B = {The first three natural numbers}

C = {a, b, c, d};

D = {d, c, a, b}

E = {a, e, i, o, u};

F = {set of vowels in English Alphabet}

i) A ……… B

ii) A …….. E

iii) C ……. D

iv) D …… F

v) F ……. A

vi) D …… E

vii) F ……. B

Answer:

i) A = B

ii) A ≠ E

iii) C=D

iv) D ≠ F

v) F ≠ A

vii) D ≠ E

viii) F ≠ B

Question 3.

In each of the following, state whether

A = B or not.

i) A = {a, b, c, d}; B = {d, c, a, b}

ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}

iii) A = (2, 4, 6, 8, 10)

B = {x: x is a positive even integer and x ≤ 10}

iv) A = {x: x ¡s a multiple of 10};

B = {10, 15, 20, 25, 30,……. }

Answer:

i) A = B because A and B have exactly the same elements i.e., a, b, c, d.

ii) A ≠ B because A and B have not exactly the same elements.

iii) A = B because A and B have exactly the same elements.

Writing B in roaster form, we have

B = {2, 4, 6, 8, 10}

iv) A = {10, 20, 30, 40,……..}

B = {10, 15, 20, 25,……..}

A ≠ B because A and B have not exactly the same elements.

Question 4.

State the reasons for the following:

i) {1,2, 3,…, 10} ≠ {x : x ∈ N and 1 < x < 10}

ii) {2, 4, 6, 8, 10} ≠ {x : x = 2n + 1 and x ∈ N}

iii) {5, 15, 30, 45} ≠ {x : x is a multiple of 15

iv) {2, 3, 5, 7, 9} ≠ {x : x is a prime number}

Solution:

The first set is {1, 2, 3, ……, 10}

Writing the second set in roaster form, we have {2, 3, 4, ……, 9}

The first set and the second set have not exactly the same elements.

∴ {1, 2, 3,……10} ≠ {x : x ∈ N and 1 < x < 10}

ii) The first set is {2, 4, 6, 8, 10}

Writing the second set in roaster form, we have {3, 5, 7, 9, ….}

∴ {2, 4, 6, 8, 10} ≠ {3, 5, 7, 9, ….}

x = 2n + 1 means x is odd.

iii) The first set is {5, 15, 30, 45}

Writing the second set in roaster form, we have {15, 30, 45, 60, …}

∴ {5, 15, 30, 45} ≠ {15, 30, 45, 60,…}

5 does not exist, since x is multiple of 15.

iv) The first set is {2, 3, 5, 7, 9}

Writing the second set in roaster form, we have {2, 3, 5, 7, 11, 13,…}

∴ {2, 3, 5, 7, 9} ≠ {2, 3, 5, 7, 11, 13 }

9 is not a prime number.

Question 5.

List all the subsets of the following sets.

i) B = {p, q}

ii) C = {x, y, z}

iii) D = {a, b, c, d}

iv) E = {1, 4, 9, 16}

v) F = {10, 100, 1000}

Solution:

i) {p}, {q}, {p, q}, { ϕ }

ii) {x}, {y}, {z}, {x, y}, {y, z}, {x, z}, {x, y, z}, {ϕ}

iii) {a}, {b}, {c}, {d}, {a, b}, {b, c}, {c, d}, {a, c}, [a, d}, {b, d}, {a, b, c}, {b, c, d}, {a, b, d}, {a, c, d}, {a, b, c, d}, {ϕ}

iv) {1}, {4}, {9}, {16}, {1, 4}, {4, 9}, {9, 16}, {1, 9}, {1, 16}, {4, 16}, {1, 4, 9}, {4, 9, 16}, {1, 4, 16}, {1, 9, 16}, {1, 4, 9, 16}, {ϕ}

v) {10}, {100}, {1000}, {10, 100}, {100, 1000}, {10, 1000}, {10, 100, 1000}, {ϕ}