NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5 is part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.5.

- Sets Class 11 Ex 1.1
- Sets Class 11 Ex 1.2
- Sets Class 11 Ex 1.3
- Sets Class 11 Ex 1.4
- Sets Class 11 Ex 1.6
- Sets Class 11 Miscellaneous Exercise

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 11 |

Subject |
Maths |

Chapter |
Chapter 1 |

Chapter Name |
Sets |

Exercise |
Ex 1.5 |

Number of Questions Solved |
7 |

Category |
NCERT Solutions |

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

**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

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