NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4 is part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4.

- Sets Class 11 Ex 1.1
- Sets Class 11 Ex 1.2
- Sets Class 11 Ex 1.3
- Sets Class 11 Ex 1.5
- 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 1.4 |

Number of Questions Solved |
12 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.4

**Question 1.**

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

**(i)** X = {1 ,3, 5}, Y= {1, 2, 3}

**(ii)** A = {a, e, i, o, u}, B = {a, b, c}

**(iii)** A = {x: x is a natural number and multiple of 3}

B = {x: x is a natural number less than 6}

**(iv)** 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

**Solution.**

**Question 2.**

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

**Solution.**

Here A = {a, b} and B = {a, b, c}. All elements of set A are present in set B.

∴ A ⊂ B. Now, A ∪ B = {a, b, c) = B.

**Question 3.**

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

**Solution.**

Here A and B are two sets such that A ⊂ B.

Take A = {1, 2} and B = {1, 2, 3}.

A ∪ B = {1, 2, 3) = B.

**Question 4.**

**If A = {11, 2, 3, 4}, B = {3, 4, 5, 6}, C={5, 6, 7, 8} and D = {7, 8, 9, 10}; find**

**(i)** A ∪ B

**(ii)** A ∪ C

**(iii)** B ∪ C

**(iv)** B ∪ O

**(v)** A ∪ B ∪ C

**(vi)** A ∪ B ∪ D

**(vii)** B ∪ C ∪ D

**Solution.**

Here A = {11, 2, 3, 4}, B = {3, 4, 5, 6}, C={5, 6, 7, 8} and D = {7, 8, 9, 10}

**Question 5.**

**Find the intersection of each pair of sets of .
**

**(i)**X = {1 ,3, 5}, Y= {1, 2, 3}

**(ii)**A = {a, e, i, o, u}, B = {a, b, c}

**(iii)**A = {x: x is a natural number and multiple of 3}

B = {x: x is a natural number less than 6}

**(iv)**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

**Solution.**

**(i)**Here X = {1, 3, 5} and Y = {1, 2, 3}

∴ X ∩ Y= {1,3}

**(ii)** Here A = {a, e, i, o, u} and B = {a, b, c}

∴ A ∩ B = {a}

**(iii)** Here A = {x: x is a natural number and multiple of 3} = {3, 6, 9,12,….} and B = {x: x is a natural number less than 6}

= {1, 2, 3, 4, 5} ∴ A ∩ B = {3}

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

**(v)** Here A = {1, 2, 3) and 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**

**(i)** A ∩ B

**(ii)** B ∩ C

**(iii)** A ∩ C ∩ D

**(iv)** A ∩ C

**(v)** B ∩ D

**(vi)** A ∩ (B ∪ C)

**(vii)** A ∩ D

**(viii)** A ∩ (B ∪ D)

**(ix)** (A ∪ B) ∩ (B ∪ C)

**(x)** (A ∪ D) ∩ (B ∪ C)

**Solution.**

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

**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**

**(i)** A ∩ B

**(ii)** A ∩ C

**(iii)** A ∩ D

**(iv)** B ∩ C

**(v)** B ∩ D

**(vi)** C ∩ D

**Solution.**

Here A = {x: x is a natural number}

= (1, 2, 3, 4, 5, …….}

B = {x: x is an even natural number}

= 12, 4, 6,………}

C = {x: x is an odd natural number}

= {1, 3, 5, 7,………}

and D = {x: x is a prime number}

= {2, 3, 5, 7,….}

**(i)** A ∩ B = {x: x is a natural number} ∩ {x: x is an even natural number}

= {x: x is an even natural number} = B.

**(ii)** A ∩ C = {x: x is a natural number} ∩ {x: x is an odd natural number}

= {x: x is an odd natural number} = C.

**(iii)** A ∩ D = {x: x is a natural number} ∩ {x: x is a prime number}

= {x: x is a prime number} = D.

**(iv)** B ∩ C = {x: x is an even natural number} ∩{x: x is an odd natural number} = φ .

**(v)** B ∩ D = [x: x is an even natural number} ∩ {x: x is a prime number} = {2}.

**(vi)** C ∩ D = {x: x is an odd natural number} ∩ {x: x is a prime number} = {x: x is an odd prime number}.

**Question 8.**

**Which of the following pairs of sets are disjoint?**

**(i)** {1, 2, 3, 4} and {x: x is a natural number and 4 ≤ x ≤ 6}

**(ii)** {a, e, i, o, u] and {c, d, e, f}

**(iii)** {x: x is an even integer} and {x: x is an odd integer}

**Solution.**

**(i)** Let A = {1,2,3,4}

and B = {x: x is a natural number and 4 ≤ x ≤ 6} = {4, 5, 6}

∴ A ∩ B = {1,2,3,4} n {4,5, 6} = {4}

Hence A and B are not disjoint sets.

**(ii)** Let A = {a, e, i, o, u} and B = {c, d, e, f}

∴ A ∩ B = {e}

Hence A and B are not disjoint sets.

**(iii)** Let A = {x : x is an even integer} and B = {x: x is an odd integer}

∴ A ∩ B = φ. Hence A and B are disjoint sets.

**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} and D = {5, 10, 15, 20}; find**

**(i)** A – B

**(ii)** A – C

**(iii)** A – D

**(iv)** B – A

**(v)** C – A

**(vi)** D – A

**(vii)** B – C

**(viii)** B – D

**(ix)** C – B

**(x)** D – B

**(xi)** C – D

**(xii)**D – C

**Solution.**

Here 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}

**(i)** A – B = {3, 6, 9, 12, 15, 18, 21} – {4, 8,12,16, 20} = {3, 6, 9,15,18, 21}

**(ii)** A – C = {3, 6, 9, 12, 15, 18, 21} – {2, 4, 6, 8, 10, 12, 14, 16} = {3, 9, 15, 18, 21}

**(iii)** A – D = {3, 6, 9, 12, 15, 18, 21} – {5,10,15, 20} = {3, 6, 9, 12, 18, 21}

**(iv)** B – A = {4, 8, 12, 16, 20} – {3, 6, 9, 12, 15, 18, 21} = {4, 8,16, 20}

**(v)** C – A = {2,4, 6, 8, 10, 12, 14, 16} – {3, 6, 9, 12, 15, 18, 21} = {2, 4, 8, 10, 14, 16}

**(vi)** D – A = {5, 10, 15, 20} – {3, 6, 9, 12, 15, 18, 21} = {5, 10, 20}

**(vii)** B – C={4, 8, 12, 16, 20} – {2, 4, 6, 8, 10, 12, 14, 16} = {20}

**(viii)** B – D = {4, 8, 12, 16, 20} – {5, 10, 15, 20} = {4, 8, 12, 16}

**(ix)** C – B = {2,4, 6, 8, 10, 12, 14, 16} – {4, 8, 12, 16, 20} = {2, 6, 10, 14}

**(x)** D – B = {5, 10, 15, 20} – {4, 8, 12, 16, 20} = {5, 10, 15}

**(xi)** C – D = {2, 4, 6, 8, 10, 12, 14, 16} – {5, 10, 15, 20} = {2, 4, 6, 8, 12, 14, 16}

**(xii)** D – C={5, 10, 15, 20} – {2, 4, 6, 8, 10, 12, 14, 16} = {5, 15, 20}

**Question 10.**

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

**(i)** X – Y

**(ii)** Y – X

**(iii)** X ∩ Y

**Solution.**

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

**(i)** X – Y = {a, b, c, d} – {f, b, d, g} = {a, c}

**(ii)** Y – X = {f, b, d, g} – {a, b, c, d} = {f, g}

**(iii)** X ∩ Y = {a, b, c, d} ∩ {f, b, d, g} = {b, d}

**Question 11.**

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

**Solution.**

We know that set of real numbers contain rational and irrational numbers. So R – Q = set of irrational numbers.

**Question 12.**

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

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

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

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

**Solution.**

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