1. Which of the following are sets? Justify your answer.(i) The colle

1.	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 100.(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.2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces:(i) 5…A (ii) 8…A (iii) 0…A(iv) 4…A (v) 2…A (vi) 10…A
Answer» (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 the criteria for determining 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 criteria for determining 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 100 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 that criteria for determining the dangerousness of an animal can vary from animal to animal. Hence, this collection is not a set. 2) (i) 5∈A, as 5 is the 5th element in set A. (ii) 8∈/A, as 8 is not present in set A. (iii) 0∈/A, as 0 is not present in set A. (iv) 4∈A, as 4 is the 4th element in set A. (v) 2∈A, as 2 is the 2nd element in set A. (vi) 10∈/A as 10 is not present in set A. 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 the criteria for determining 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 criteria for determining 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 100 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 the most dangerous animals of the world is not a well-defined collection because the criteria for determining the dangerousness of an animal can vary from person to person. Hence, this collection is not a set. 2. If the element belongs to A we write ∈,else ∉ (i) 5 ∈ A, as 5 is the 5th element in set A. (ii) 8 ∉ A, as 8 is not present in set A. (iii) 0 ∉ A, as 0 is not present in set A. (iv) 4 ∈ A, as 4 is the 4th element in set A. (v) 2 ∈ A, as 2 is the 2nd element in set A. (vi) 10 ∉ A as 10 is not present in set A.

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 100.(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.2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces:(i) 5…A (ii) 8…A (iii) 0…A(iv) 4…A (v) 2…A (vi) 10…A

Answer»

(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 the criteria for determining 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 criteria for determining 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 100 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 that criteria for determining the dangerousness of an animal can vary from animal to animal.
Hence, this collection is not a set.

(i) 5∈A, as 5 is the 5th element in set A.
(ii) 8∈/A, as 8 is not present in set A.
(iii) 0∈/A, as 0 is not present in set A.
(iv) 4∈A, as 4 is the 4th element in set A.
(v) 2∈A, as 2 is the 2nd element in set A.
(vi) 10∈/A as 10 is not present in set A.

(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.