NCERT Solutions for Class 11th Maths Exercise 1.4 Set

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CBSE NCERT Solutions For Class 11th Maths Chapter 1 : Set. NCERT Solutins For Class 11 Mathematics. Exercise 1.1, Exercise 1.2, Exercise 1.3, Exercise 1.4, Exercise 1.5, Exercise 1.6,  (Miscellaneous Excercise) many more solutions

Exercise 1.4

Question 1:

Find the union of each of the following pairs of sets:

  1. X = {1, 3, 5} Y = {1, 2, 3}
  2. A = {a, e, i, o, u} B = {a, b, c}
  3. A = {x: x is a natural number and multiple of 3} B = {x: x is a natural number less than 6}
  4. A = {x: x is a natural number and 1 < x ≤ 6}

B = {x: x is a natural number and 6 < x < 10}

(v) A = {1, 2, 3}, B = Φ

Answer

  1. X = {1, 3, 5} Y = {1, 2, 3} X∪ Y= {1, 2, 3, 5}
  2. A = {a, e, i, o, u} B = {a, b, c}

A∪ B = {a, b, c, e, i, o, u}

(iii) A = {x: x is a natural number and multiple of 3} = {3, 6, 9 …} As B = {x: x is a natural number less than 6} = {1, 2, 3, 4, 5, 6} A ∪ B = {1, 2, 4, 5, 3, 6, 9, 12 …}

∴ A ∪ B = {x: x = 1, 2, 4, 5 or a multiple of 3}

(iv) A = {x: x is a natural number and 1 < x ≤ 6} = {2, 3, 4, 5, 6} B = {x: x is a natural number and 6 < x < 10} = {7, 8, 9}

A∪ B = {2, 3, 4, 5, 6, 7, 8, 9}

∴ A∪ B = {x: x ∈ N and 1 < x < 10}

(v) A = {1, 2, 3}, B = Φ A∪ B = {1, 2, 3}

Question 2:

Let A = {a, b}, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?

Answer

Here, A = {a, b} and B = {a, b, c}

Yes, A ⊂ B.

A∪ B = {a, b, c} = B

Question 3:

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

Answer

If A and B are two sets such that A ⊂ B, then A ∪ B = B.

Question 4:

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

  1. A ∪ B
  2. A ∪ C
  3. B ∪ C
  4. B ∪ D
  5. A ∪ B ∪ C
  6. A ∪ B ∪ D

(vii) B C D

Answer

A = {1, 2, 3, 4], B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}

  1. A ∪ B = {1, 2, 3, 4, 5, 6}
  2. A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}
  3. B ∪ C = {3, 4, 5, 6, 7, 8}
  4. B ∪ D = {3, 4, 5, 6, 7, 8, 9, 10}
  5. A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}
  6. A ∪ B ∪ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
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(vii) B C D = {3, 4, 5, 6, 7, 8, 9, 10}

Question 5:

Find the intersection of each pair of sets:

  1. X = {1, 3, 5} Y = {1, 2, 3}
  2. A = {a, e, i, o, u} B = {a, b, c}
  3. A = {x: x is a natural number and multiple of 3} B = {x: x is a natural number less than 6}
  4. A = {x: x is a natural number and 1 < x ≤ 6}

B = {x: x is a natural number and 6 < x < 10}

(v) A = {1, 2, 3}, B = Φ

Answer

    1. X = {1, 3, 5}, Y = {1, 2, 3} X ∩ Y = {1, 3}
    2. A = {a, e, i, o, u}, B = {a, b, c} A ∩ B = {a}
      1. A = {x: x is a natural number and multiple of 3} = (3, 6, 9 …} B = {x: x is a natural number less than 6} = {1, 2, 3, 4, 5}
  • A ∩ B = {3}
      1. A = {x: x is a natural number and 1 < x ≤ 6} = {2, 3, 4, 5, 6} B = {x: x is a natural number and 6 < x < 10} = {7, 8, 9}

A ∩ B = Φ

      1. A = {1, 2, 3}, B = Φ

A ∩ B = Φ

Question 6:

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find

  1. A ∩ B
  2. B ∩ C
  3. A ∩ C ∩ D
  4. A ∩ C
  5. B ∩ D
  6. A ∩ (B ∪ C)
  7. A ∩ D
  8. A ∩ (B ∪ D)
  9. (A ∩ B) ∩ (B ∪ C)
  10. (A ∪ D) ∩ (B ∪ C) Answer
    1. A ∩ B = {7, 9, 11}
    2. B ∩ C = {11, 13}
      1. A ∩ C ∩ D = { A ∩ C} ∩ D = {11} ∩ {15, 17} = Φ
      2. A ∩ C = {11}
      3. B ∩ D = Φ
      4. A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
  • {7, 9, 11} ∪ {11} = {7, 9, 11}
      1. A ∩ D = Φ
      2. A ∩ (B ∪ D) = (A ∩ B) ∪ (A ∩ D)
  • {7, 9, 11} ∪ Φ = {7, 9, 11}
      1. (A ∩ B) ∩ (B ∪ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}
      2. (A ∪ D) ∩ (B ∪ C) = {3, 5, 7, 9, 11, 15, 17) ∩ {7, 9, 11, 13, 15}
  • {7, 9, 11, 15}
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Question 7:

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

  1. A ∩ B
  2. A ∩ C
  3. A ∩ D
  4. B ∩ C
  5. B ∩ D
  6. C ∩ D Answer

A = {x: x is a natural number} = {1, 2, 3, 4, 5 …}

B ={x: x is an even natural number} = {2, 4, 6, 8 …} C = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}

D = {x: x is a prime number} = {2, 3, 5, 7 …}

  1. A ∩B = {x: x is a even natural number} = B
  2. A ∩ C = {x: x is an odd natural number} = C
  3. A ∩ D = {x: x is a prime number} = D
  4. B ∩ C = Φ
  5. B ∩ D = {2}
  6. C ∩ D = {x: x is odd prime number}

Question 8:

Which of the following pairs of sets are disjoint

  1. {1, 2, 3, 4} and {x: x is a natural number and 4 ≤ x ≤ 6}
  2. {a, e, i, o, u}and {c, d, e, f}
  3. {x: x is an even integer} and {x: x is an odd integer} Answer
    1. {1, 2, 3, 4}

{x: x is a natural number and 4 ≤ x6} = {4, 5, 6} Now, {1, 2, 3, 4} ∩ {4, 5, 6} = {4}

Therefore, this pair of sets is not disjoint.

(ii) {a, e, i, o, u} (c, d, e, f} = {e}

Therefore, {a, e, i, o, u} and (c, d, e, f} are not disjoint.

(iii) {x: x is an even integer} {x: x is an odd integer} = Φ Therefore, this pair of sets is disjoint.

Question 9:

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

  1. A – B
  2. A – C
  3. A – D
  4. B – A
  5. C – A
  6. D – A
  7. B – C
  8. B – D
  9. C – B
  10. D – B
  11. C – D
  12. D – C Answer
    1. A – B = {3, 6, 9, 15, 18, 21}
    2. A – C = {3, 9, 15, 18, 21}
  13. A – D = {3, 6, 9, 12, 18, 21}
  14. B – A = {4, 8, 16, 20}
  15. C – A = {2, 4, 8, 10, 14, 16}
  16. D – A = {5, 10, 20}
  17. B – C = {20}
  18. B – D = {4, 8, 12, 16}
  19. C – B = {2, 6, 10, 14}
  20. D – B = {5, 10, 15}
  21. C – D = {2, 4, 6, 8, 12, 14, 16}
  22. D – C = {5, 15, 20}
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Question 10:

If X = {a, b, c, d} and Y = {f, b, d, g}, find

  1. X – Y
  2. Y – X
  3. X ∩ Y Answer
    1. X – Y = {a, c}
    2. Y – X = {f, g}

(iii) X Y = {b, d}

Question 11:

If R is the set of real numbers and Q is the set of rational numbers, then what is RQ? Answer

R: set of real numbers Q: set of rational numbers

Therefore, R – Q is a set of irrational numbers.

Question 12:

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

  1. {2, 3, 4, 5} and {3, 6} are disjoint sets.
  2. {a, e, i, o, u } and {a, b, c, d} are disjoint sets.
  3. {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
  4. {2, 6, 10} and {3, 7, 11} are disjoint sets. Answer
    1. False

As 3 ∈ {2, 3, 4, 5}, 3 ∈ {3, 6}

⇒ {2, 3, 4, 5} ∩ {3, 6} = {3}

(ii) False

As a ∈ {a, e, i, o, u}, a ∈ {a, b, c, d}

⇒ {a, e, i, o, u } ∩ {a, b, c, d} = {a}

(iii) True

As {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ

(iv) True

As {2, 6, 10} ∩ {3, 7, 11} = Φ

NCERT Solutions for Class XI Maths: Chapter 1 – Set



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