AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 2 Sets Ex 2.2 Textbook Questions and Answers.

## AP State Syllabus SSC 10th Class Maths Solutions 2nd Lesson Sets Exercise 2.2

## 10th Class Maths 2nd Lesson Sets Ex 2.2 Textbook Questions and Answers

Question 1.

If A = {1, 2, 3, 4}; B = {1, 2, 3, 5, 6} then find A ∩ B and B ∩ A. Are they equal ?

Answer:

Given sets are A = {1, 2, 3, 4} and B = {1,2,3, 5,6}

A ∩ B = {1,2, 3,4} ∩ {1,2, 3, 5, 6}

= {1,2,3} …… (1)

B ∩ A = {1, 2, 3, 5, 6} ∩ {1, 2, 3, 4}

= {1,2,3} …….(2)

From (1) and (2)

A ∩ B and B ∩ A are same.

Question 2.

A = {0, 2, 4}, find A ∩ φ and A ∩ A. Comment.

Answer:

Given set A = {0, 2, 4} and φ is a null set.

A ∩ φ = {0, 2, 4} ∩ { }

= { } ……. (1)

A ∩ A = {0, 2, 4} ∩ {0, 2, 4}

= {0, 2,4} …….. (2)

From (1) and (2),

We conclude that A ∩ φ = φ and A ∩ A = A

Question 3.

If A = {2, 4, 6, 8, 10} and B = {3, 6, 9, 12, 15}, find A – B and B – A.

Answer:

Given sets are

A {2, 4, 6, 8, 10} and B = {3, 6, 9, 12, 15}

A – B = {2, 4, 6, 8, 10} – {3, 6, 9, 12, 15}

= {2, 4, 8, 10} …… (1)

B – A = {3, 6, 9, 12, 15} – {2, 4, 6, 8, 10}

= {3, 9, 12, 15} …… (2)

From (1) and (2), A – B ≠ B – A

Question 4.

If A and B are two sets such that A ⊂ B then, what is A ∪ B?

Answer:

Let us consider A ⊂ B

Set A = {1, 2, 3} and

Set B = {1, 2, 3, 4, 5}

Now A ∪ B = {1, 2, 3} ∪ {1, 2, 3, 4, 5}

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

∴ A ∪ B = B

Question 5.

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}

Find A ∩ B, A ∩ C, A ∩ D, B ∩ C, B ∩ D, C ∩ D.

Answer:

Given sets are

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ……}

B = {2, 4, 6, 8, 10, …….}

C = {1, 3, 5, 7, 9, …….}

D = {2, 3, 5, 7, 11, …….}

A ∩ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …….} ∩ {2, 4, 6, 8, 10, ……}

= {2, 4, 6, 8, 10, ……}

A ∩ C = {1, 2, 3,4, 5, 6, 7, 8, 9, 10, …} ∩ {1, 3, 5, 7, 9 }

= {1, 3, 5, 7, 9, ……}

A ∩ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …} ∩ {2, 3, -5, 7, 11,….}

= {2, 3, 5, 7, 11, ……}

B ∩ C = {2, 4, 6, 8, 10, ……} ∩ {1, 3, 5, 7, 9, …….}

= { } = φ

B ∩ D = {2, 4, 6, 8, 10, ……} ∩ {2, 3, 5, 7, 11, ……}

= {2}

C ∩ D = {1, 3, 5, 7, 9, ……} ∩ {2, 3, 5, 7, 11, 13, ……}

= {3, 5, 7, …..}

Question 6.

If A = {3, 6, 9, 12, 15, 18, 21}; B = {4, 8, 12, 16, 20}; C = {2, 4, 6, 8, 10, 12, 14, 16}; D = {5, 10, 15, 20} find

(i) A – B

(ii) A – C

(iii) A – D

(iv) B – A

(v) C – A

(vi) D – A

(vii) B – C

(viii) B – D

(ix) C – B

(x) D – B

Answer:

Given sets are A = {3, 6, 9, 12, 15, 18, 21}

B = {4, 8, 12, 16, 20}

C = {2, 4, 6, 8, 10, 12, 14, 16} and

D = {5, 10, 15, 20}

i) A – B = {3, 6, 9, 12, 15, 18, 21} – {4, 8, 12, 16, 20} = {3, 6, 9, 15, 18, 21}

ii) A – C = {3, 6, 9, 12, 15, 18, 21} – {2, 4, 6, 8, 10, 12, 14, 16} = {3,9,15,18,21}

iii) A – D = {3, 6, 9, 12, 15, 18, 21} – {5, 10, 15, 20} = {3,6,9,12,18,21}

iv) B – A = {4, 8, 12, 16, 20} – {3, 6, 9, 12, 15, 18, 21} = {4, 8, 16, 20}

v) C – A = {2, 4, 6, 8, 10, 12, 14, 16} – {3, 6, 9, 12, 15, 18, 21} = {2, 4, 8, 10, 14, 16}

vi) D – A = {5, 10, 15, 20} – {3, 6, 9, 12, 15, 18, 21} = {5, 10, 20}

vii) B – C = {4, 8, 12, 16, 20} – {2, 4, 6, 8, 10, 12, 14, 16} = {20}

viii) B – D = {4, 8, 12, 16,20} – {5, 10, 15, 20} = {4, 8, 12, 16}

ix) C – B = {2, 4, 6, 8, 10, 12, 14, 16} – {4, 8, 12, 16, 20} = {2, 6, 10, 14}

x) D – B = {5, 10, 15, 20} – {4, 8, 12, 16, 20} = {5, 10, 15}

Question 7.

State whether each of the following statement is true or false. Justify your answers.

i) {2,3,4,5} and {3,6} are disjoint sets.

ii) {a, e, i, o, u} and {a, b, c, d} are disjoint sets.

iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.

iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.

Answer:

i) Rule: If two sets are disjoint their intersection is null set.

= {2, 3, 4, 5} n {3, 6} = { 3 } ≠ φ

∴ Given statement is False.

ii) Given sets are

{a, e, i, o, u} and {a, b, c, d}

= {a, e, i, o, u} ∩ {a, b, c, d}

= { a } ≠ φ

∴ Given statement is False.

iii) Given sets are

{2, 6, 10, 14} and {3, 7, 11, 15}

= {2, 6, 10, 14} ∩ {3, 7, 11, 15}

= { }

∴ Given statement is True.

iv) Given sets are

{2, 6, 10} and {3, 7, 11}

= {2, 6, 10} ∩ {3, 7, 11} = { }

∴ Given statement is True.