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Class 11 RD Sharma Solutions – Chapter 1 Sets – Exercise 1.1
  • Last Updated : 03 May, 2021

Question 1. What is the difference between a collection and a set? Give reasons to support your answer.

Solution:

A collection represents a group of objects. Whereas well-defined collections are called sets. Only unique elements can be present in a set.

Example: The collection of good novels is not a set. But, if we consider Good Novels in Rohan’s bookshelf, then it is a set. As contains the defined books that Rohan considers good, whereas a collection of good novels might be subjective.

Thus, we can say that every set is a collection, but every collection is not necessarily a set. Only well-defined collections are sets.

Question 2. Which of the following collections are sets? Justify your answer:

(i) A collection of all natural numbers less than 50.



(ii) The collection of good hockey players in India.

(iii) The collection of all the girls in your class.

(iv) The collection of all talented writers of India.

(v) The collection of difficult topics in Mathematics.

(vi) The collection of novels written by Munshi Prem Chand.

(vii) The collection of all questions of this chapter.

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

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



(x) The collection of prime integers.

Solution:

(i) Yes, it’s a set. Since, there are well-defined natural number less than 50, so it is a set.

(ii) No, it’s not a set. Since, good hockey players in India can be subjective depending from person to person, so it is not a set. 

(iii) Yes, it’s a set. Since, there are a well-defined number of girls in a class, so it is a set.

(iv) No, it’s not a set. Since, whether a writer is talented or not can be a subjective opinion varying from one person to another, so it is not a set.

(v) No, it’s not a set. Since, the term ‘difficult’ is not well-defined. A topic may be difficult for one person, but may not be difficult for another person.

(vi) Yes, it’s a set. Since, there is a definite collection of novels written by Munshi Prem Chand, so it is a set.

(vii) Yes, it’s a set. Since, the number of questions belonging to a specific chapter will be a definite quantity, so it is a set.

(viii) Yes, it’s a set. Since, a collection of all months of a year beginning with the letter J is a definite quantity, so it is a set.



(ix) No, it’s not a set. Since, the term ‘most dangerous’ is subjective and not well-defined, so it’s not a set.

(x) Yes, it’s a set. Since, the collections of prime integers is a definite quantity, so it’s a set.

Question 3. If A = {0,1,2,3,4,5,6,7,8,9,10}, then insert the appropriate symbol or in each of the following blank spaces:

(i) 4 ……A

(ii) -4……A

(iii) 12…..A

(iv) 9…..A

(v) 0……A

(vi) -2……A

Solution:

(i) 4 ……A

Since, 4 is present in set A,

Therefore, 4 ∈ A

(ii) -4……A

Since, -4 is not present in set A,

Therefore, -4 ∉ A

(iii) 12…..A

Since, 12 is not present in set A,

Therefore, 12 ∉ A

(iv) 9…..A

Since, 9 is present in set A,

Therefore, 9 ∈ A

(v) 0……A

Since, 0 is present in set A,

Therefore, 0 ∈ A

(vi) -2……A

Since, -2 is not present in set A,

Therefore, -2 ∉ A

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