# NCERT Solutions For Class 11 Maths Chapter 1 Sets Ex 1.5

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 1 |

Exercise | Class 11 Maths Chapter 1 Sets Exercise 1.5 |

Number of Questions Solved | 7 |

## NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5

**NCERT TEXTBOOK EXERCISES**

**Ex 1.5 Class 11 Maths 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**

**(i)** A’**(ii)** B’**(iii)** (A ∪ C)’**(iv)** (A ∪B)’**(v)** (A’)’**(vi)** (B – C)’

**Solution.**

Here 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}**(i)** A’=U – A

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

= {5, 6, 7, 8, 9}

**(ii)** B’=U – B

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

= {1, 3, 5, 7, 9}

**(iii)** A ∪ C = {1, 2, 3, 4} ∪ {3, 4, 5, 6}

= (1, 2, 3, 4, 5, 6}

(A∪C)’=U-(A∪C)

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

= {7, 8, 9}

**(iv)** A ∪ B = {1, 2, 3,4} ∪ {2, 4, 6, 8}

= {1, 2, 3, 4, 6, 8}

(A∪B)’ = U – (A∪B)

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

= {5, 7, 9}

**(v)** We know that A’ = {5, 6, 7, 8, 9}

(A’)’ =U – A’

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

= {1, 2, 3, 4}

**(vi)** B – C = {2, 4, 6, 8} – {3, 4, 5, 6} = {2, 8}

(B-C)’=U – (B-C)

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

= {1, 3, 4, 5, 6, 7, 9}.

**Ex 1.5 Class 11 Maths Question 2. If U = {a,b, c, d, e, f, g, h}, find the complements of the following sets:**

**(i)** A = {a, b, c}**(ii)** B = {d, e, f, g}**(iii)** C = {a, c, e, g}**(iv)** D = {f, g, h, a}

**Solution.**

**(i)** A’ = U – A = {a, b, c, d, e, f, g, h} – {a, b, c}

= {d, e,f, g, h}

**(ii)** B’ = U – B = {a, b, c, d, e,f, g, h} – {d, e, f, g}

= {a, b, c, h}

**(iii)** C’ = U – C = {a, b, c, d, e, f, g, h} – {a, c, e, g}

= {b, d, f, h}

**(iv)** D’ = U – D = {a, b, c, d, e, f, g, h} – {f, g, h, a}

= {b, c, d, e}.

**Ex 1.5 Class 11 Maths Question 3. Taking the set of natural numbers as the universal set, write down the complements of the following sets:**

**(i)** {x: x is an even natural number}**(ii)** {x: x is an odd natural number}**(iii)** {x: x is a positive multiple of 3}**(iv)** {x: x is a prime number}**(v)** {x: x is a natural number divisible by 3 and 5}**(vi)** {x: x is a perfect square}**(vii)** {x: x is a perfect cube}**(viii)** {x: x + 5 = 8}**(ix)** (x: 2x + 5 = 9)**(x)** {x: x ≥ 7}**(xi)** {x: x ∈ W and 2x + 1 > 10}

**Solution.**

**Ex 1.5 Class 11 Maths 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)** (A ∪ B)’ = A’∩B’**(ii) **(A ∩ B)’ = A’∪B’

**Solution.**

**Ex 1.5 Class 11 Maths Question 5. Draw appropriate Venn diagram for each of the following:**

**(i)** (A ∪ B)’**(ii)** A’∩B’**(iii)** (A ∩ B)’**(iv)** A’ ∪ B’

**Solution.**

**Ex 1.5 Class 11 Maths 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 A’?**

**Solution.**

Here U = {x : x is a triangle}

A = {x: x is a triangle and has at least one angle different from 60°}

∴ A’ = U – A = {x : x is a triangle} – {x : x is a triangle and has atleast one angle different from 60°}

= {x : x is a triangle and has all angles equal to 60°)

= Set of all equilateral triangles.

**Ex 1.5 Class 11 Maths Question 7. Fill in the blanks to make each of the following a true statement:**

**(i)** A ∪ A’ = **…….****(ii)** φ’ ∩ A = .**…….****(iii)** A ∩ A’ =** …….****(iv)** U’ ∩ A = .**…….**

**Solution.**

**(i) **A ∪ A’= U**(ii)** φ’ ∩ A = U ∩ A = A**(iii)** A ∩ A’ = φ**(iv)** U’ ∩ A = φ ∩ A = φ

## NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.5 PDF

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