10th Maths Sets Exercise 2.2 Solutions

Exercise 2.2 Solutions – Class X Mathematics

Exercise 2.2 Solutions – Class X Mathematics

These solutions are based on the Telangana State Class X Mathematics textbook, focusing on set operations. Mathematical expressions are rendered using MathJax.

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

A ∩ B = {x : x ∈ A and x ∈ B} = {1, 2, 3}.
B ∩ A = {x : x ∈ B and x ∈ A} = {1, 2, 3}.
Since A ∩ B = B ∩ A, they are equal.

A ∩ B = {1, 2, 3}, B ∩ A = {1, 2, 3}, Equal: Yes

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

A ∩ φ = {x : x ∈ A and x ∈ φ} = φ (empty set).
A ∩ A = {x : x ∈ A and x ∈ A} = {0, 2, 4}.
Comment: A ∩ φ is always the empty set, and A ∩ A is the set itself.

A ∩ φ = φ, A ∩ A = {0, 2, 4}

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

A – B = {x : x ∈ A and x ∉ B} = {2, 4, 8, 10}.
B – A = {x : x ∈ B and x ∉ A} = {3, 9, 12, 15}.

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

4. If A and B are two sets such that A ⊆ B then what is A ∪ B?

If A ⊆ B, every element of A is in B.
A ∪ B = {x : x ∈ A or x ∈ B} = B (since A is a subset of B).

A ∪ B = B

5. Let 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 and C ∩ D.

A = {1, 2, 3, …}, B = {2, 4, 6, …}, C = {1, 3, 5, …}, D = {2, 3, 5, 7, …}.
A ∩ B = {x : x ∈ A and x ∈ B} = {2, 4, 6, …} = B.
A ∩ C = {x : x ∈ A and x ∈ C} = {1, 3, 5, …} = C.
A ∩ D = {x : x ∈ A and x ∈ D} = {2, 3, 5, 7, …} = D.
B ∩ C = {x : x ∈ B and x ∈ C} = φ (no number is both even and odd).
B ∩ D = {x : x ∈ B and x ∈ D} = {2} (only 2 is even and prime).
C ∩ D = {x : x ∈ C and x ∈ D} = {3, 5, 7, …} (odd primes).

A ∩ B = {2, 4, 6, …}, A ∩ C = {1, 3, 5, …}, A ∩ D = {2, 3, 5, 7, …}, B ∩ C = φ, B ∩ D = {2}, C ∩ D = {3, 5, 7, …}

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} and D = {5, 10, 15, 20}, find (i) A – B (ii) A – C (iii) A – D (iv) B – A (v) C – A (vi) B – D (vii) B – C (viii) C – B (ix) C – D (x) D – B.

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}.
A – B = {3, 6, 9, 15, 18, 21} (exclude 12).
A – C = {3, 9, 15, 18, 21} (exclude 6, 12).
A – D = {3, 6, 9, 12, 18, 21} (exclude 15).
B – A = {4, 8, 16, 20} (exclude 12).
C – A = {2, 4, 8, 10, 14, 16} (exclude 6, 12).
B – D = {4, 8, 12, 16} (exclude 20).
C – B = {2, 6, 10, 14} (exclude 4, 8, 12, 16, 20).
C – D = {2, 4, 6, 8, 12, 14, 16} (exclude 10, 20).
D – B = {5, 10, 15} (exclude 20).

(i) A – B = {3, 6, 9, 15, 18, 21}, (ii) A – C = {3, 9, 15, 18, 21}, (iii) A – D = {3, 6, 9, 12, 18, 21}, (iv) B – A = {4, 8, 16, 20}, (v) C – A = {2, 4, 8, 10, 14, 16}, (vi) B – D = {4, 8, 12, 16}, (vii) B – C = {}, (viii) C – B = {2, 6, 10, 14}, (ix) C – D = {2, 4, 6, 8, 12, 14, 16}, (x) D – B = {5, 10, 15}

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

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

Common element: 3.
Not disjoint as they share 3.

Conclusion: False

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

Common element: a.
Not disjoint as they share a.

Conclusion: False

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

No common elements.
Disjoint as they have no elements in common.

Conclusion: True

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

No common elements.
Disjoint as they have no elements in common.

Conclusion: True

Author

Leave a Comment