**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, wether 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 ……ASince, 4 is present in set A,

Therefore,

4 ∈ A

(ii) -4……ASince, -4 is not present in set A,

Therefore,

-4 ∉ A

(iii) 12…..ASince, 12 is not present in set A,

Therefore,

12 ∉ A

(iv) 9…..ASince, 9 is present in set A,

Therefore,

9 ∈ A

(v) 0……ASince, 0 is present in set A,

Therefore,

0 ∈ A

(vi) -2……ASince, -2 is not present in set A,

Therefore,

-2 ∉ A

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