AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 2 Sets Ex 2.3 Textbook Questions and Answers.

## AP State Syllabus SSC 10th Class Maths Solutions 2nd Lesson Sets Exercise 2.3

### 10th Class Maths 2nd Lesson Sets Ex 2.3 Textbook Questions and Answers

Question 1.

Which of the following sets are equal?

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

ii) B = {x : x is a letter in the word FLOW}

iii) C = {x : x is a letter in the word WOLF}

Answer:

i) Elements in set A are {F, L, O, W}

ii) Elements in set B are {F, L, O, W}

iii) Elements in set C are {F, L, O, W} Sets A, B and C have same elements, Hence, they are equal sets.

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

vi) D ≠ E

vii) 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 is a multiple of 10}; B = {10, 15, 20, 25, 30, …}

Answer:

i) A = B

ii) A ≠ B

iii) A ≠ B

iv) A ≠ B

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}

Answer:

i) In R.H.S ‘x’ is greater than 1 and less than 10 but L.H.S is having both 1 and 10.

ii) L.H.S ≠ R.H.S

R.H.S: x = 2n + 1 is definition of odd numbers.

L.H.S: Given set is even numbers set.

iii) x is a multiple of 15.

So 5 does not exist.

iv) x is a prime number but 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}

Answer:

i) Subsets of ‘B’ are {p}, {q}, {p, q}, φ

ii) Subsets of ‘C’ are {x}, {y} {z}, {x, y}, {y, z}, {z, x}, {x, y, z} and φ (2^{3} = 8)

iii) Subsets of ‘D’ are {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} and φ

iv) Subsets of ‘E’ are

φ, {1}, {4}, {9}, {16}, {1,4}, {1,9}, {1, 16}, {4, 9}, {4, 16}, (9, 16}, {1, 4, 9}, {1, 9, 16}, {4, 9, 16}, {1, 4, 16}, {1, 4, 9, 16}

v) Subsets of ‘F’ are

φ, {10}, {100}, {1000}, {10, 100}, {100, 1000}, {10, 1000}, {10, 100, 1000}.