# CBSE Class 11-Mathematics: Natural Numbers: Sets Exercise 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 1**:

Which of the following are sets? Justify your answer.

(i) The collection of all months of a year beginning with the letter J.

(ii) The collection of ten most talented writers of India.

(iii) A team of eleven best-cricket batsmen of the world.

(iv) The collection of all boys in your class.

(v) The collection of all-natural numbers less than .

(vi) A collection of novels written by the writer Munshi Prem Chand.

(vii) The collection of all even integers.

(viii) The collection of questions in this Chapter.

(ix) A collection of most dangerous animals of the world.

**Question 2**:

Let . Insert the appropriate symbol or in the blank spaces:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

**Question 3**:

Write the following sets in roster form:

(i) .

(ii) .

(iii)

(iv) .

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER.

**Question 4**:

Write the following sets in the set-builder form:

(i)

(ii)

(iii)

(iv)

(v)

**Question 5**:

List all the elements of the following sets:

(i)

(ii)

(iii)

(iv)

(v)

(vi) .

**Question 6**:

Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

(I)

(II)

(III)

(IV)

**Solution 1**:

(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects because one can definitely identify a month that belongs to this collection.

Hence, this collection is a set.

(ii) The collection of ten most talented writers of India is not a well-defined collection because determination of a writer՚s talent may vary from person to person.

Hence, this collection is not a set.

(iii) A team of eleven best cricket batsmen of the world is not a well-defined collection because the determination a batsman՚s talent may vary from person to person.

Hence, this collection is not a set.

(iv) The collection of all boys in your class is a well-defined collection because you can definitely identify a boy who belongs to this collection.

Hence, this collection is a set.

(v) The collection of all natural numbers less than is a well-defined collection because one can definitely identify a number that belongs to this collection.

Hence, this collection is a set.

(vi) A collection of novels written by the writer Munshi Prem Chand is a well-defined collection because one can definitely identify a book that belongs to this collection.

Hence, this collection is a set.

(vii) The collection of all even integers is a well-defined collection because one can definitely identify an even integer that belongs to this collection.

Hence, this collection is a set.

(viii) The collection of questions in this chapter is a well-defined collection because one can definitely identify a question that belongs to this chapter.

Hence, this collection is a set.

(ix) The collection of most dangerous animals of the world is not a well defined collection because the determination of the dangerousness of an animal can vary from person to person.

Hence, this collection is not a set.

**Solution 2**:

. The answer are quite apparent

(i) as belongs to A

(ii) as does not belongs to A

(iii) A as does not belongs to A

(iv) as does belongs to A

(v) as does belongs to A

(vi) as does not belongs to A

**Solution 3**

1 | The elements of this set are and only. Therefore, the given set can be written in roster form as | |

2 | The elements of this set are and only. Therefore, the given set can be written in roster form as | |

3 | The numbers whose sum is can be So The elements of this set are , and only. Therefore, this set can be written in roster form as | |

4 | The elements of this set are , and 5 only. Therefore, this set can be written in roster form as | |

5. | The set of all letters in the word TRIGONOMETRY | There are letters in the word TRIGONOMETRY, out of which letters T, R, and O are repeated. Therefore, this set can be written in roster form as |

6. | The set of all letters in the word BETTER | There are 6 letters in the word BETTER, out of which letters E and T are repeated. Therefore, this set can be written in roster form as |

**Solution 4**:

1 | ||

2 | It can be seen that and | |

3 | It can be seen that and . | |

4 | ||

5 | It can be seen that . |

**Solution 5**:

1 | ||

2 | As. and , the only integer are | |

3 | Given that taking root both sides we get Integers number between and including and are , and Hence | |

4 | Word LOYAL has alphabet L, O, Y and A Hence | |

5 | Month of year having days are February, April, June, September and November. Hence | |

6 | Consonant in the English alphabet before alphabet are , and . Hence |

**Solution 6**:

(i) All the elements of this set are natural numbers as well as the divisors of 6

Therefore, (i) matches with (c) .

(ii) It can be seen that 2 and 3 are prime numbers. They are also the divisors of 6.

Therefore, (ii) matches with (a) .

(iii) All the elements of this set are letters of the word MATHEMATICS.

Therefore, (iii) matches with (d) .

(iv) All the elements of this set are odd natural numbers less than 10.

Therefore, (iv) matches with (b) .