Chapter – 1
Sets
Ex 1.1
Class 11 Maths
Q.1: Which of the following are sets. Explain your answer.
(a). The collection of all day in a week which have the first letter S.
(b). The collection of ten most famous singers of India.
(c). A group of best football strikers of the world.
(d). The collection of all girls in your school.
(e). The collection of all odd numbers below 50.
(f). A collection of poems written by the poet Shakespeare.
(g). The collection of all prime numbers.
(h). The collection of questions in science book.
(i). A collection of most dangerous reptiles in India.
Solution:
(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 identity a month that belongs to this collection. Hence, this collection is a set.
(ii) The collection of ten most talented writer of India is not a well-defined collection because the criteria for determining a writer’s talent 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 the criteria for determining the dangerousness of an animal can vary from person to person. Hence, this collection is not a set.
Q.2: Let P = {2, 3, 4, 5, 6, 7}. Insert the correct symbol ∈or∉ inside the given blank spaces below:
(a). 2 . . . . . . . . . . P
(b). 9 . . . . . . . . . P
(c). 11 . . . . . . . . P
(d). 4 . . . . . . . . P
(e). 0 . . . . . . . . P
(f). 7 . . . . . . . . P
Solution:
(i) 5 ∈ A
(ii) 8 ∉ A
(iii) 0 ∉ A
(iv) 4 ∈ A
(v) 2 ∈ A
(vi) 10 ∉ A
Q.3: Write the given sets in roster form:
(a). P = {y: y is an integer and -4 < y < 6}.
(b). Q = {y: y is a natural number which is <8}
(c). R = {y: y is a 2 digit natural number in which the sum of its digits is 9}
(d). S = {y: y is a prime number which is a divisor of 70}
(e). T = The set of all letters in the word ELEPHANT(f). U = The set of all letters in the word DIVISION
Solution:
(i) A = {x: x is an integer and –3 < x < 7}The elements of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6 only.Therefore, the given set can be written in roster form asA = {–2, –1, 0, 1, 2, 3, 4, 5, 6}
(ii) B = {x: x is a natural number less than 6}The elements of this set are 1, 2, 3, 4, and 5 only.Therefore, the given set can be written in roster form asB = {1, 2, 3, 4, 5}
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}The elements of this set are 17, 26, 35, 44, 53, 62, 71, and 80 only.Therefore, this set can be written in roster form asC = {17, 26, 35, 44, 53, 62, 71, 80}
(iv) D = {x: x is a prime number which is a divisor of 60}