NCERT Solutions for Class 11th Maths Exercise 1.5 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 1.5

Question 1:

Let U ={1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find

Answer

U ={1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {1, 2, 3, 4}

B = {2, 4, 6, 8}

C = {3, 4, 5, 6}

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Question 2:

If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:

  1. A = {a, b, c}
  2. B = {d, e, f, g}

  1. C = {a, c, e, g}
  2. D = {f, g, h, a} Answer

U = {a, b, c, d, e, f, g, h}

  1. A = {a, b, c}
  2. B = {d, e, f, g}
  3. C = {a, c, e, g}
  4. D = {f, g, h, a}

Question 3:

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Taking the set of natural numbers as the universal set, write down the complements of the following sets:

  1. {x: x is an even natural number}
  2. {x: x is an odd natural number}
  3. {x: x is a positive multiple of 3}
  4. {x: x is a prime number}
  5. {x: x is a natural number divisible by 3 and 5}
  6. {x: x is a perfect square}
  7. {x: x is perfect cube}
  8. {x: x + 5 = 8}
  9. {x: 2x + 5 = 9}
  10. {x: x ≥ 7}
  11. {x: x ∈ N and 2x + 1 > 10}

Answer

U = N: Set of natural numbers

(i) {x: x is an even natural number}´ = {x: x is an odd natural number}

  1. {x: x is an odd natural number}´ = {x: x is an even natural number}
  2. {x: x is a positive multiple of 3}´ = {x: x ∈ N and x is not a multiple of 3}
  3. {x: x is a prime number}´ ={x: x is a positive composite number and x = 1}
  4. {x: x is a natural number divisible by 3 and 5}´ = {x: x is a natural number that is not divisible by 3 or 5}
  5. {x: x is a perfect square}´ = {x: x ∈ N and x is not a perfect square}
  6. {x: x is a perfect cube}´ = {x: x ∈ N and x is not a perfect cube}
  7. {x: x + 5 = 8}´ = {x: x ∈ N and x ≠ 3}
  8. {x: 2x + 5 = 9}´ = {x: x ∈ N and x ≠ 2}
  9. {x: x ≥ 7}´ = {x: x ∈ N and x < 7}
  10. {x: x ∈ N and 2x + 1 > 10}´ = {x: x ∈ N and x ≤ 9/2}
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Question 4:

If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that

(i) (ii)

Answer

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {2, 4, 6, 8}, B = {2, 3, 5, 7}

(i)

(ii)

Question 5:

Draw appropriate Venn diagram for each of the following:

Answer

(i)

(ii)

(iii)

(iv)

Question 6:

Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is ?

Answer

is the set of all equilateral triangles.

Question 7:

Fill in the blanks to make each of the following a true statement:

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(i) (ii) Φ′ A = …

(iii)

(iv)

Answer

(i)

(ii) Φ′ A = U A = A

∴ Φ′ ∩ A = A

  1. A ∩ A′ = Φ
  2. U′ ∩ A = Φ ∩ A = Φ

∴ U′ ∩ A = Φ

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