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

Set guarantees that the collection will contain unique elements (no duplicates). A Collection does not guarantee this. The Set interface contains only methods inherited from Collection and adds the restriction that duplicate elements are prohibited. Two Set instances are equal if they contain the same elements.

$\\$

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 girls in your class.

iv) The collection of most talented writers in India

v) The collection of difficult topics in Mathematics

vi) The collection of all months of a year beginning with the letter $J$.

vii) A collection of novels written by Munshi Prem Chand

viii) The collection of all questions in this chapter.

ix) A collection of most dangerous animals of the world

x) The collection of prime integers

i) A collection of all-natural numbers less than $50$: It is a SET because it is WELL DEFINED.

ii) The collection of good hockey players in India: It is NOT a SET because it is NOT WELL DEFINED. We don’t know what good hockey player mean and different people may consider different players as good.

iii) The collection of all girls in your class: It is a SET because it is WELL DEFINED. We will know exactly how many girls we have in the class and also their names.

iv) The collection of most talented writers in India: It is NOT a SET because it is NOT WELL DEFINED. We don’t know what talented writers mean or look like.

v) The collection of difficult topics in Mathematics: It is NOT a SET because it is NOT WELL DEFINED. Topics may be easy or difficult based on the student.

vi) The collection of all months of a year beginning with the letter $J$: It is a SET because it is WELL DEFINED. We can write the set as $\{ January, June, July \}$

vii) A collection of novels written by Munshi Prem Chand: It is a SET because it is WELL DEFINED. We know exactly the number and names of novels written by Munshi Prem Chand.

viii) The collection of all questions in this chapter: It is a SET because it is WELL DEFINED. We know the questions listed in this chapter.

ix) A collection of most dangerous animals of the world: It is NOT a SET because it is NOT WELL DEFINED. We don’t know what the definition of dangerous animals is. Some animals might be dangerous to an individual but not to others.

x) The collection of prime integers: It is a SET because it is WELL DEFINED. We can write the set as $\{ 2, 5, 7, \cdots \}$

$\\$

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

i) $4 \cdots A$     ii) $-4 \cdots A$     iii) $12 \cdots A$

vi) $9 \cdots A$     v) $0 \cdots A$     vi) $-2 \cdots A$

i) $4 \in A$     ii) $-4 \notin A$     iii) $12 \notin A$
vi) $9 \in A$     v) $0 \in A$     vi) $-2 \notin A$
$\\$