TS 10th Class Maths Solutions Chapter 2 Sets Ex 2.2

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Students can practice TS 10th Class Maths Solutions Chapter 2 Sets Ex 2.2 to get the best methods of solving problems.

TS 10th Class Maths Solutions Chapter 2 Sets Exercise 2.2

Question 1.
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then find A ∩ B and B ∩ C. Are they same ?
Solution:
A = {1, 2, 3, 4}; B = {1, 2, 3, 5, 6}
∴ A ∩ B = {1, 2, 3, 4} ∩ {1, 2, 3, 5, 6}
= {1, 2, 3}
B ∩ A = {1, 2, 3, 5, 6} ∩ {1, 2, 3, 4)
= {1, 2, 3}
Yes, A ∩ B and B ∩ A are same.

Question 2.
A = {0, 2, 4}, find A ∩ ϕ and A ∩ A. Comments. (June 15(A.P.))
Solution:
A = {0, 2, 4}
A ∩ ϕ = {0, 2, 4} ∩ ϕ
= ϕ
A ∩ A = {0, 2, 4} ∩ {0, 2, 4}
= {0, 2, 4} = A

TS 10th Class Maths Solutions Chapter 1 Sets Ex 2.2

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

Question 4.
If A and B are two sets such that A ⊂ B then what is A ∪ B?
Solution:
Let us consider A ⊂ B.
Set A = {1, 2, 3}
Set B = {1, 2, 3, 4, 5}
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}
D = {x : x is a prime number
Find A∩B, A∩C, A∩D, B∩C, B∩D, C∩D.
Solution:
A = {1, 2, 3, 4, …….. }
B = {2, 4, 6, 8, ……….}
C = {1, 3, 5,7, ……….}
D = {2, 3, 5, 7, ……….}
A ∩ B = {1, 2, 3, 4,………. } ∩ {2, 4, 6, 8,………. }
= {2, 4, 6,…… }
= {even natural numbers)
A ∩ C = {1, 2, 3, 4,……} ∩ {1, 3, 5,……}
= {1, 3, 5,………}
= {odd natural numbers}
A ∩ D = {1, 2, 3, 4,……} ∩ {2, 3, 5, 7, ……..}
= {2, 3, ………}
= {prime natural numbers}
B ∩ C = {2, 4, 6, 8,…..} ∩ {1, 3, 5, 7, …….}
= ϕ
= Null set (Or) empty set
B ∩ D = {2, 4, 6, 8,…….. } ∩ {2, 3, 5, 7,…….. }
= {2} = {even natural number}
C ∩ D = {1, 3, 5, 7,……. } ∩ {2, 3, 5, 7,…….}
= {3, 5, 7,…….. }
= {All odd prime numbers)

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
Solution:
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}

TS 10th Class Maths Solutions Chapter 1 Sets Ex 2.2

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:
Two sets are said to be disjoint sets when they have no elements in common.
i) In the given two sets. ‘3’ is common. So, they are not disjoint sets. Hence, the given statement is false.
ii) In the given two sets, ‘a’ is common. So, they are not disjoint sets. Hence, the given statement is false.
iii) There are no elements common in the given two sets. So they are disjoint sets. Hence, the given statement is true.
iv) There are no elements common in the given two sets, So they are disjoint sets. Hence. the given statement is true.

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